I just booked such a flight (AS operating as HA) for December on the Alaska website. At least the Alaska site allows you to put your AA number in the booking. The HA website only recognizes HA numbers.

It is not allowing me (EXP) any benefits in booking even "preferred" seats much less extra comfort seats. I'll wait a few hours to see if the information flows through (I am not expecting it to) and will probably cancel tomorrow within the 24 hours. I figured it was the fastest way to find out.

According to the AS website "Atmos" elites are entitled to all the various perks, including preferred seating and upgrades, that AS members have historically had on AA flights. But it does not appear to work the other way, at least with respect to the former HA flights.

As I said, not expecting anything but wanted to find out directly.

Edited to add: as we all knew / assumed, no benefits. When I pulled up the booking on the AS website this morning to look at seats, it said "you're flying with our partner" and pushed me to the HA website. And no change there.