I've done a similar offline connection at SFO 6 months ago - though connecting to SFO-SEA on AS instead.
If I recall correctly, immediately past customs, there is a conveyor belt that takes already-tagged bags to your connecting flight. The only baggage counter I remember seeing was for United - but not Alaska. It looked like I would have had to bring my bag to the regular Alaska check in, so I didn't bother and just carried it on for my next flight.