Do ACs have Marriott preference, even if it comes from a Marriott deposit? I don't know the answer. Can you see the studio with a non Marriott deposit? If so, I would think that the AC should be able to pull it. It is a studio after all. ACs from a deposit usually have the most pull and are just about unrestricted inside 59 days. If any restrictions are there, I would think that the only units they perhaps couldn't see are the larger units.
If you can't see the week with a Marriott deposit, I would suspect that the Marriott preference is keeping you from getting it.