The time of year that you are going plays into how likely you are to have your request met. If they are not totally booked, then they have a little more flexibility. Also, the time of day that you check in can be a factor.
That being said --- I would think that you would have a really good chance of your request being met if all you are asking for is to be in the Mansions area. You really are not asking for a lot. The more specific you are (i.e., a certain floor, a certain building, some people even request a certain room), the narrower your chances get.
I suggest that you have your preference noted on your reservation. Then, when you check in, if they happen to give you Alligator Bayou, just ask if Mansions is available. If you are willing to wait for a room to be ready, let them know that. I would check in as early as possible and be willing to wait for a Mansions room to be ready.