Do Alaska MVP Gold members have any advantages for seating assignments on BA flights?

I see that oneworld Gold and Silver get free selection at the time of booking, but can't tell if there are any reciprocal benefits for Mileage Plan members. This might have some effect on whether I book an upcoming transatlantic flight on American vs. British Airways.

Sorry if this is covered elsewhere, Google wasn't helpful in finding an answer (so I'm assuming the benefit doesn't exist).