Can you back the bow after final tillering?

Absolutely. That's when I usually do it, when it's about done being tillered and prior to final sanding. Snake skins are decorative only and shouldn't change the tiller or draw weight at all... unless it's a super thick anaconda or something.

I usually wait until a bow is shot in before adding skins. I want to be sure it will survive and is worthy the additional work and expense of adding snake skins.

Question: totally off topic but can you put snake skin under clear glass on a r/d glass bow? And follow up where is a good place to buy skins?

It really depends on how thick and smooth the skin is. Most folks, unless they order a commercial bow with skins on it, just add it to the back of the bow over the glass.

I say always shoot in the bow before adding the skins. I've waisted probably about 3 sets of skins over the years by prematurely snaking the bow.

Is it still a self-bow if you add a snakeskin backing?

Yes. Snake skins are only decorative with no added performance. Some snakes skins, like anacondas and boas can add a bit of protection because of their thickness so I'd call a bow with those skins on them a backed selfbow like one with rawhide backing.