Yeah, they can, but it's my understanding that it's unlikely due to the difficulty of finding all the passive mobs in a ten-chunk area. That's not too hard in a biome like plains, but in the jungle, it's no easy task. As far as I know, if you've even missed one chicken than wandered down into the mouth of a cave, there won't be any new passive mobs spawn.
The area depends on your render distance plus the spawn chunks, of which a 16x16 chunk area is always loaded, so if you have your render distance set to 32 you'd have to kill every passive mob within a 65x65 chunk area in addition to the spawn chunks; on the other hand, a render distance of 2 would be great for making more passive mobs spawn; just by moving around a bit you could spawn at least 10 mobs (so, no, a single missed chicken won't kill off mob spawning) within each 5x5 chunk area (for comparison, during world generation there is a 10% chance per chunk of a pack of up to 4 mobs in most chunks (7% in a few biomes, none in river/ocean or if water covers the entire chunk), meaning that the spawn chunks alone may have 100 or more passive mobs, a 5x5 chunk averages 10 mobs, and a 65x65 chunk area averages 1690 mobs).
Jungles have the additional issue of ocelots, which can vastly exceed any mob cap because while they are passive mobs and count towards the passive mob cap they spawn under the hostile mob cap, meaning that they can significantly exceed either cap (in jungles where I've explored all the caves the entity count climbs into the 300+ range and ocelots are everywhere. Only the fact they can despawn prevents them from accumulating indefinitely). Fortunately, they have a very low chance of spawning, particularly since 1.7 (1/10 as often), so as long as hostile mobs can freely spawn they will be rare. However, hostile mobs (and ocelots) attempt to spawn 400 times more often than passive mobs so they could still spawn fast enough to fill the cap; if they are an issue you can fill the hostile mob cap to prevent them from spawning.