What is the setting?
If it's Golarion there are quite a few other factors impacting it. For starters, while the Qlippoth hate all Demons with an enormous passion they would, most likely, hate lawful invaders of their ancestral homes even more.
If the cosmic balance starts to shift then the Aeons would also come into play, working alongside (not with) the demons in this case.
The Daemons, who created the first demons, would probably also make a move though what they would do I'm not sure of.
What also might cause some issues is that both sides would actually have a full fledged deity on their side.
As for the material plane, do note that while Asmodeus has an entire country devoted to him Lamashtu actually counts many monstrous races among her followers and she has many cults as well.