So slight variation on what you are doing, but I did SEA-YVR-LHR a week ago. SEA-YVR as a normal ticket on AS, YVR-LHR as a mileage ticket. At checkin I asked AS to interline my baggage with BA so that I would not have to deal with claiming luggage at YVR. They processed the bags through and when I landed at YVR I simply stayed in the international departure section. The only check they do is to make sure that you have a valid international boarding pass onward. When we landed at LHR our bags popped out as expected.