316 will take a razor edge but won't hold it very long...it's not really worth it. Better to get a good cutting edge and leave it a bit rough. It's heavy, though, and it is pretty suseptible to rust, so don't expect it to be weatherproof and I would think it best to keep the points on the small side.
I will say, though, that I've never made broadheads out of 316...just knives...lots of knives.