On several occasions over the last ten years, I've checked bags in with American that connected to a BA flight on a different ticket and then onwards from LHR to Stockholm ona third ticket. No problems - except for having to insist that the bags were tagged for ARN - checkin staff at Dayton hadn't a clue which Stockholm airport I was going to, or that there was more than one!
I'm expecting to use Alaska Airlines in May to go to Seattle and then onwards on BA to LHR, and expect to check a bag right through.