From recent experience it seems the systems are integrated enough to know that you're a Summit. I just bought a ticket on YX for a Frontier flight and it assigned me a seat (I'm Ascent, and if the system didn't know that, it presumably wouldn't have assigned one).

I also enjoy the fare "competition" (funny since both airlines are under common ownership, not like a true codeshare between competitors)...I paid $100 for the Midwest flight when Frontier wanted $152 for the same seat!