I believe it depends on the ticketed fare code, but at least seats in the back of the plane should be free, as the AS website states.

BTW: it seems impossible to select paid seats (e.g. the extra legroom ones) with an AS-coded FI flight (AS awards will be FI-coded so should not have that problem). Only once OLCI opens that is possible. One of the reasons I intend never to fly them again (main reason is using short-haul planes for rather long flights).

[added later] just realised the OP asks about reward flights, all I said above was related to paid codeshare flights. I would not be surprised if that wording on the AS website only applies to revenue bookings on AS's website.