I believe the question in the OP, is whether or not Imhoteps draining would be to much for Wolverine to contend with. I believe Wolverines healing won't be able to keep up with Imhotep because Imhoteps draining was magical in nature. Now could Wolverine recover from the ordeal, absolutely, but he won't imo regrow tissue as fast as Imhotep drains it.
We only see the speed of his devouring (from what I remember) twice, first film we see the shadow of it from I think the second theif. The mummy returns we actually get to see it. Is he devouring your life force? Because his healing factor can't deal with that. And would he get wolverine's healing factor? Not that he would really need it anyway, cause with his powers he's immortal.
Well, going by the fact that the Silver Samurai was draining his healing factor (after it had already been restored), and visibly aging him, this thread is not looking good for Logan. Add in the fact that Imhotep is magical, and it makes things even more uncertain. We have no idea how well his healing factor responds to magic.