There will likely be an active link from MX A to Switch A, and an active link from MX B to Switch A; both the links to Switch B will be blocking. There won't be a loop (you are correct in saying that if both links to MX A were active then there would be a loop).
EDIT: I say 'likely' as you can never quite be sure which ports will get Blocked by spanning tree as you don't know the actual port costs; you can take a good guess, but sometimes an unexpected port gets blocked.