I was looking into volunteering at SDACC but it didn't seem like there was much of anything veterinary we could do there, just lots of dog walking. I've heard something about people needing to get 100 hours of dog walking and then you are allowed to shadow in the hospital there? Not sure though, never looked into it because I didn't have a car at the time. I volunteered at the SF SPCA during school breaks and got to do a lot there in the shelter hospital wards, we had a ringworm going around in all the cats during the summer, but I think that was probably a pretty unique shelter with better vet facilities than most.
I've heard lots of good things about Project Wildlife and know several people who have volunteered there, I know you learn a ton and it's probably much more hands on (animal care, though, not vet)... they only have a vet come there every once in a while. You start at a pretty low level there and they have a lot of worksheets and training that you go thru to work your way up to doing different things. Looks pretty cool, I wish I had time to do everything! So it really depends if you want to do shelter or wildlife. And if you need vet experience for applying to vet school, neither of those will count, at least not Project Wildlife and not SDACC until you actually get working under the supervision of a vet, they just fall under animal experience.