It will take some work, but it's perfectly doable.
Enemies with special defenses
The players won't have access to see invisible, flight, magic weapons, or ghost touch. Therefore, if you include enemies that can fly, or have DR/magic, or are intangible, these will be huge challenges, and may be downright impossible. The easy solution is simply to not include such enemies, but the more interesting way is to treat them as nigh-invulnerable enemies that the heroes will have to figure out how to defeat. In a normal Pathfinder game, a ghost is a normal critter with a +2 CR template pasted on top, and requires some minimal preparation to defeat. In a low-magic Pathfinder game, a ghost is a mystery: why did they become a ghost? How can you persuade them to pass on, or at least let the party pass by peacefully? Can you persuade the local priest to perform an exorcism, and will it even work? Instead of "find monster, insert fireball," these types of encounters are now role-playing challenges, because they can't be solved any other way!
Alternatively, you can simply strip out the special defenses from enemies. Pathfinder assumes you have level-appropriate counters to special abilities anyway, so by removing those special defenses, you aren't going too far from the original intent. Adjusting the CR is left as an exercise for the GM, because it's going to take a fair amount of trial-and-error to determine what the right balance is.
Fixing armor class, and other numbers issues
Pathfinder assumes that both attack bonuses and defenses will be augmented by magic items. This partially balances out if the players don't have magic items, but consider giving everyone a +1 bonus to AC and all defenses every four levels. Don't make them pay a feat for it, just give it to them.
While you're at it, give your players bonus XP for the monsters they defeat, by calculating the XP as if the monsters were a higher CR. Since they're operating without magic, every encounter is going to be harder than what the DMG "expects" when it calculates XP per CR.
What will they do with their money?
Your players won't be able to buy gear that personally enhances their ability to make things dead faster, or grant them new solutions. If you keep to the normal loot rules, then the party will have far, far more money than they know what to do with. You have two options here: give them less money, or give them something to do with that money.
Let them invest in mercenary companies or land holdings. Let them become influential in the church, or their hometown, or even their country as their economic might and donations in the right places give them power that they would never be able to take with a sword. Favors in high places give characters some very powerful options.
Recovery after combat
This will require explicit house rules; you'll need to accelerate natural healing (heal a percentage of HP per day instead of a flat amount?), allow Heal checks to do much more than they normally do, grant the local clergy some extremely localized healing powers (they can heal people brought to their church, but not outside of their place of worship), and/or make this a political game rather than a hack-and-slash game.
If everyone's having fun, then it's a good game. It doesn't matter if the characters aren't optimized: as long as they feel like they're making a difference in the world and they're enjoying the game, then you're doing it right. The characters will be balanced, more or less: they all don't have access to magic, so intra-party balance isn't as much of a problem. You'll see that the players lack all of the magic-based solutions that you'd expect in a normal Pathfinder game, and you'll select the enemies more carefully, but things will work out fine. Let your players know that things will be a bit different than normal, and your players will go along with it; they requested this kind of game, after all.
Best Answer
Having run stable 13-player groups (with everyone showing up every week, no less) in several systems, a large group has 4 issues:
1) face time for every player
2) Synergy of group size.
3) Appropriate challenges for the group as a whole
4) GM communications
1 Face Time
Now, my big group for D&D3.X was 9 players, not 13, but finding challenges (especially given the average level was 10th) was minor compared to just making certain every player got some face time twice or more every session. That was handled best by simply having NPC's target different PC's for their interactions; in other words, not leaving it to the players to decide who interacts with a given NPC.
2 Synergy
The synergy effect comes from overlapping skills and the help rules. Which said, the help rules in 3.x are pretty weak, but they do add up. Further, with large groups in 3.X, you'll tend to get more over-the-top combat potential due to players having similar roles.
3 Challenges
The challenge issue is an evolution of the synergy issue. Remember - not every monster is intended to be the "ideal party" challenge; many are really balanced for an ideal party but are taken out mostly by one member of said party, often the wizard or the fighter. (Keeping in mind: ideal party is 1 fighter, 1 wizard or sorcerer, 1 cleric, and 1 rogue.) Most are fighter based - and my experience is that large parties tend to be heavy on fighters and wizards, light on rogues and clerics, and having few of anything else. So, often, combats will depend on how competent the targeted players are.
Further, fights with a few large monsters tend to become very one-sided when the first big-bad goes down, as those resources fighting it get diverted to the others. That's normal; it's just more obvious in larger groups.
Some specific cases to remember:
Undead: aimed at clerics, especially the incorporeal ones. Balance the encounter based upon the party being the level of your clerics, and sized at 4x your number of clerics. Simpler undead, like skeletons, who present no conversion issues, can be used to protect the higher level undead from turning, but also can be taken out by fighters and combat wizards easily.
Incorporeal anything: clerics and wizards - the fighters are close to useless. For large groups, always give the fighters something to face that's corporeal.
potent monsters: many monsters are highly potent - some surprisingly so - such as Illithids and Beholders. Don't add more to balance them; add subservient fighters instead. Beholders, for example, should usually be solitary - to buff it up, add enslaved kobolds or orcs, or a couple lucky rounds will be a snowball effect.
4 Communication with the GM
The solutions vary by group, but mostly break down to turn taking or collating. Usually in some combination. Some additional options
4a Collating Actions
By collating, this means a small number of players talk to the GM, but tell the GM what their and several other players' characters are doing; it is a variation on the single "caller" of AD&D rules fame.
The classic solution was to run the game as a minis wargame, with ONE player collecting/collating everyone's actions. It works, but it can be unsatisfying. It is, however, how E. Gary Gygax ran parties of up to 20 players.
4b Turn Taking
Simply make certain that turn taking isn't just in combat. When it comes time to get actions, go around and pointedly ask each player for what they're doing. Much above 5 players, the traditional popcorning of actions no longer is viable, as the noise it generates becomes considerable, and too much gets missed.
4c Harlequins
A Harlequin is a player who plays only NPCs. They don't narrate, don't resolve game rules, and don't get special authority. They are a real challenge for some groups, but in larger groups can be spectacularly successful at reducing the GM overload.
This is especially true in certain types of play. For example, in one large (13 player, 25 PC), I had a 14th player who couldn't show regularly. When he did, he got to play NPC's. If he was negotiating with the players, I'd give him a list of what his allowed resources were, and turn him loose with the away team sent to deal with him. Meanwhile, I'd do the GM-needed interactions to solve the overlapping mechanical problem of the week. And when done, he'd note down the final resolved issue.
Further, Harlequins allow the GM to have really GOOD dialogue from multiple NPC's.
The drawbacks are that many can't make the distinction between assistant GM and Harlequin. It can be set onto a continuum, where certain situations the harlequin is allowed to call for certain rolls, and that works, but once they start calling for rolls for anything other than affecting the character they play, they're really into being assistant GM's.
4d Assistant GM's
The problem with an assistant GM is trust. You HAVE to trust them not to muck up your adventure. The benefit is that you don't have to run the whole group all the time, and if the party splits, you take one part and they take the other.
Assistant GM's are best made from harlequins, not experienced GM's. Start letting the harlequin players call for rolls, and slowly build them up to being part of the resolution in general.
It's very important not to have the assistant GM's contradict your calls, but likewise, if it's not a rules issue, if they make a call, back it up.
5 Problem Players
Some types of players tend to be problems in certain groups... the classics being Rules Lawyers, Attention Hounds, and Shy Guys.
5A The Rules Lawyer
Co-opting the rules lawyer to assistant GM is great in minis-mode, not so good in story mode. Leave him/her as a normal player, but ask them for advice on rules issues. Don't make them officially assistant GM's.
5b The Attention Hound
The Attention Hound really works well as a harlequin. It puts him in the center of things, but also keeps him from eating your time as GM.
5c The Shy Guy
This is the guy who shows up, but doesn't really speak up. The kind who act only when asked, "What's your character doing?"
The shy guy, in a small group, can be coaxed by the GM into playing. In a large group, they often fall by the wayside. The trick is often to have another player prompt them; in some cases, having them be the caller for a small portion of the group can break them out of their hesitance.