Assuming you mean that animals didn't cease existing, which would assuredly cause an impossible to imagine ecological collapse especially by the loss of pollinators, and that we instead as a species developed an instant and total intolerance to consume meat...
Yeah, probably pretty easily once we adjusted agricultural practices to emphasis more proteins and the like. We use huge amounts of acreage for fodder for animals, so all that could be cut back and focused on growing something else. Our food production for humans would assuredly increase as a result.
If all non-human animals died, we'd likely suffer a significant population loss but still survive.
Irregardless, for all intensive purposes, I could care less.