i would say no, its not a "special effect" of the bite.
it is similar to a feat, where you hit, you can try to trip. you don't hit you can't try to trip.
the special effect of an attack is basically like poison, disease, etc. where you have to pierce the creature's skin, to get to use it.
where as the trip would be like you grabbing a chunk of fur, and attempt to put the creature off balance, where it doesn't matter if the creature took damage or not