I'm pretty sure you have to do the Move Up before you check your bag, and that once the bag is checked, you can't do a Move Up any more.
My Mr and I just had a hilarious conversation about the hypthetical terrorist blowing up the wrong plane because the airline lost his bags. I think the whole concept is, if YOU want to be separated from your bags (or increase the chances that the airline will do that for you), it's a red flag, but if it's done without the passenger's knowledge or request, it's less likely that you're trying to blow something up and not blow yourself up with it. I'm not saying that logic is right, although that's exactly what happened in Air India 182--- passenger checked a bomb in his bag then no-showed for the flight; it was a bit more complicated as he requested a multiple-carrier interline on two reservations that were not on the same PNR.