I hunted 22 and C once back in 2004 and I haven't been back since. We had a good hunt and made it happen, but it wasn't easy. At that time I thought it was easier to find a decent buck then it was to find a decent goat on public land. It is easier to find private land to hunt goats on then deer though. You really have to think about what dates you want to be there as portions of C are open for Deer at different times. If you are deer hunting, look for the deepest nastiest canyons you can find and there will be some deer hanging out there, you can jump them up like rabbits.
It really depends what you are looking for. If a 13 inch long, 70 inch goat will make you happy I'd say it is possible and if a 150 inch buck would make you happy, it might be possible. Neither will be easy. It will be fun, but not easy.