AA will gladly check your bag all the way thru CMH-LAX-SEA; however, as you noted, AS may pull it at LAX if they match bags to passengers and you're not on board
iirc AS Baggage Service at SEA is pretty good about moving unclaimed bags into a secure area, but there's no guarantee that they will do so in a timely manner ... while people can -- either accidentally or maliciously -- walk off with others' bags from carousels pretty much any time, knowingly leaving your bag unclaimed for a couple days could be inviting this to happen