No, Warlock Spellslots do not count toward the Multiclass Spellcaster table
Spell Slots. You determine your available spell slots
by adding together all your levels in the bard, cleric,
druid, sorcerer, and wizard classes, half your levels
(rounded down) in the paladin and ranger classes, and
a third of your fighter or rogue levels (rounded down)
if you have the Eldritch Knight or the Arcane Trickster
feature. Use this total to determine your spell slots by
consulting the Multiclass Spellcaster table. - PHB p. 164
Warlock isn't included in that list. Thus you would only have 2 1st level spells as a level 19 warlock, level 1 wizard PC. You could cast level 1 warlock spells using your wizard slots and cast known level 1 wizard spells using your pact magic. Granted you would be able to cast those level 1 spells at maximum level (as per usual with pact magic) but its not going to benefit you in comparison to Eldritch Master which allows you to double your spells per day effectively.
Problem?
In this particular case, nothing. Any concern you might have about "overpowered" is mitigated by his stats being at unimpressive levels. From your previous question you indicate that the players are not leaning toward min-max, power gaming, nor optimization in a munchkinny way. He's using finesse weapons that in time may limit highest damage potential: but if they aren't in min max mode, that does not seem to matter to the group.
At higher levels, he may get a little frustrated with melee damage since there are no two-handed finesse weapons and there are fewer choices in weapons ... but a lot of that gets into what fighting styles he uses and chooses. (And you control what magical weapons, if any, become available so you can tailor that to this party/team. Our DM did just that for our Bard, who is a rapier using singer).
At higher levels he'll benefit from those Divine Smite nova shots. When paired with sneak attacks from his rogue levels, he should be able to keep his damage in a "good enough" zone if the party fights well as a team.
The other place a low Strength would be a Paladin issue is in armor selection: if he wants Chain, Splint or Plate, he needs 13 / 15 / 15 strength respectively. With the proposed Dex build and Rogue multiclass, he's unlikely to want them since they give Disadvantage on Stealth checks. He can wear Breastplate with no minimum Strength requirement -- allows up to +2 of his Dex AC bonus, and no disadvantage for stealth. At 400 GP it may be a level or two before he can afford it. A 50 GP chain shirt may be his best for the time being.
From @Ethan's comment: With leather armor, a shield, and 20 Dex (After a ASI's) he will end up with 19 AC, 1 lower than full plate+shield, but the Piradin will be good at all +Dex skills. This makes for solid function when full plate isn't a good idea -- such as waterborne adventures. His damage output will be identical to a strength based shield using paladin (barring difference in MC class features).
If this is a role and story based move, all the more reason to go with it. It sounds like fun - which is why we play. As long as the player knows where the difficulties are up front with the stats as is, the player is taking on a challenge. Good on 'em!
I'd recommend a ruling to let him proceed as desired. (And if later on they finds some gauntlets of ogre strength ... )
Best Answer
It's all the same.
The amount of XP you need to go from Fighter 3 to Fighter 4 is the same amount of XP you need to go from Fighter 3 to Fighter 3/Druid 1: 1800 xp.
See the "Character Advancement" table (as referenced in the quote above) on page 15 of the Player's Handbook. And when you read it, note that the XP numbers listed are total XP, not how much more you need on top of your existing XP to get to that level. So 3rd level to 4th is 2700 − 900 = 1800 more XP, not 2700 more XP.