No.

Spell-like Abilities (SLAs) are "very much like spells", but they aren't spells. While they behave the same way as spells in regards to antimagic fields, dispelling, spell resistance or causing attacks of opportuinty as they're cast, they can't be counterspelled and they have no V, S or M components for instance.

As such, it should be necessary to explicitly name SLAs when willing to negate them. While we can speculate that they work the same way as spells, nowhere it is told that they are affected by the same things (otherwise, they would probably behave the same way even for counterspelling or components) - there are also enough cases of naming them separately into an effect to enforce the effect on them (see Styphon's answer) to exclude the hypotesis of the developers failing to tell us that whatever works on spells also works on SLAs if not explicitly noted.

Acquiring an antimagic field

The typical wizard must be level 11 to cast the 6th-level spell antimagic field, but once he can, the rogue could commission from him magic items. It's even possible that when the wizard hits level 11, the wizard takes the feat Craft Staff, and a staff is the easiest and cheapest way for the rogue to use the skill Use Magic Device to cast consistently the spell antimagic field, but the rogue must find means to recharge the staff when it's depleted. The cost to create a staff of antimagic field is 26,700 gp, which includes the 300 gp for the masterwork staff. (The base price for a scroll of antimagic field (6th-level arcane spell at caster level 11) is 1,650 gp if the rogue only wants to use the spell once.)

Without many other items that create an effect like the spell antimagic field, the equalizer shield (120,830 gp; 23 lbs.) appears to be the item to use when ballparking prices for similar items that create an effect like the spell antimagic field. The fact that without the equalizer shield's ability to create an antimagic field once per day the equalizer shield is just a +1 mithral tower shield means the game puts the price of the ability to generate an antimagic field on command once per day at upwards of 100,000 gp.

Adjudicating an antimagic field

The spell antimagic field's spell level belies its vast power; it's one of the most powerful and difficult to manage effects in the game. It allows the defeat of many foes the PCs would've otherwise found invincible, and it allows the weak foes to defeat the PCs. It's a nuclear weapon that sends all users back to the Stone Age time of No Magic, and that's scary. Even creatures who plan around the spell can be hurt by the spell's unpredictability; the nature of PCs' adventures rarely make adventuring without magic a good idea.

To that end, I agree with Ciacciu's answer: experiment. Start with a scroll or two and see how it changes your game, and remember to let the foes do the same.