Interesting question! I would say that in the absence of any suitably qualified medical personnel, a vet would be better than any Joe Bloggs but humans have different anatomy, different drug dose requirements and different surgical implements would be needed. Animals also have different tolerances to certain drugs/food items than us so will they have that knowledge about what is appropriate in a human?
Also when Vets treat animals, they work on a basis of elimination and assumption as you can't have a conversation with an animal but you can with a human (well normally) and that has pros and well as cons.
I know in the UK vets cannot treat humans unless it is a true emergency situation and I think that would be on a good Samaritan basis. In a life‑or‑death scenario, the law generally protects good‑faith attempts to save a life as with first aiders—but only then. It maybe different elsewhere in the world.
As to removing a bullet, removing the bullet, depending where it is, maybe achievable but its what had happened to the rest of the body as the bullet has pushed through it that may be the real medical emergency. And again indepth knowledge of anatomy and the correct surgical instruments may be a deal breaker.
But hey, if I was laying in a battlefield injured, I would be grateful for a vet if that was all there was.