It depends on how they ;separate'. I'll try and keep this as minimally political as I can.
If Quebec enters in a sovereignty association type-agreement in a legal referendum recognized by the Canadian government with all of Quebec territory intact, I see few problems emerging with regards to a Quebec team. I think in the short-term post-referendum the NHL would be wary of moving a team to a new country without first seeing how the transition of authority would play out. If again it was some form of sovereignty-association they'd keep the same currency, keep many of the favorable trade contracts- it would essentially be like Quebec now with an international border and perhaps one a bit more conscious over its spending habits. A Quebec City team would still be viable- and if they finish the arena I see no major roadblocks to expanding there beyond a brief waiting period to make sure that it's stable (and it would be fine). The only outstanding issue would be language, which I'm sure the NHL could find a work around for (and any team in Quebec is likely to draft heavily from the province anyway). Likewise, Montreal would have few problems. The name "Canadien" is still used in Quebec and refers to French Canadians, and I highly doubt it could be changed, Habs fans would be in uproar. Separatists outside of Greater Montreal would probably flock to a Quebec team anyway.
If it's full independence, some form of partition (outside the North) or a 'worst-case scenario' sovereignty (bad referendum, bad blood b/w Canada/Quebec) I can see the NHL being much more wary of expanding there. Depending on what happens, Quebec, Montreal or neither could be affected directly (partition is probably the worst case scenario for both teams), but indirectly through the economy or political tensions (travel visas, etc.) If independence went
bad there'd probably be a crisis among many francophones in the league as well, having to likely choose between a Canadian and/or Quebec identity. Let me emphasize that this is a
bad scenario: just listing what
could hypothetically happen not what must happen, will happen or I believe should happen.
I actually think that Quebec sovereignty-association, if it happened, would be far more like the former and would make for quite the Olympic rivalry (and temporarily blow up Canada's olympic team

).