Short Answer: No. If his regeneration has any relationship to the actual biological processes of terrestrial beings, without oxygen he should eventually slow down and stop moving as the fuel of organic life on Earth is utilized through oxygen use. Would he be dead? Unlikely, he has jump-started his biological processes in the past, I would assume if presented with oxygen his body would start right up.
Longer Answer: The mechanics of Wolverine's regeneration are poorly defined. As such we are forced to take certain ideas since they have already been portrayed as feats in the X-franchise books, for granted.
Logan is able to:
- As long as there is a single cell (I suppose it needs a nucleus and cellular data to engage his supercharged cellular mitosis) return from being nearly obliterated.The time needed for this complete regeneration has not been defined.
- Returning from such a state can temporarily erase his memory but those memories return to him over time.
- He does not need to consume any mass to regenerate damaged tissues. So no matter how much mass is displaced from his body, he can, without consuming new mass, regenerate his tissues.
- This would also imply his body can restart itself without a complete nervous or active nervous system, literally jump-starting himself from death.
- (Q: Where does his consciousness reside during this time...)
Despite Wolverine's ability to regenerate tissue without having consumed mass, he still seems to have basic biological processes like eating, drinking, and respiration. Are they truly necessary? It has not been determined that he does not need to eat, only that he can survive for a long time without food.
Since he still appears to need to breathe, it is likely putting him into an area without air, would eventually starve his body of much needed oxygen. How long he could maintain his operation without oxygen might be longer than a normal human, but if he uses oxygen like normal humans, he would eventually require oxygen.
Without it his cells would eventually shut down and await refueling. This should drive him into a coma-like state. He would not be dead, seeing how as soon as his body was exposed to oxygen, he would revive, but he would not be mobile, either.
If the take the other approach and say he does not need to breathe, then his powers begin to border on the supernatural or require a completely new framework to be used to define them.