If you can hold a room with no cancellation fee then there's no real harm in holding one outside the housing process then going through the housing process later to see if you can do better.
Things to keep in mind...
1. You are going to pay more for it, but if you get the hotel you want it might be worth it to you.
2. Make sure you are not going to be charged a cancellation fee if you are going to try this. Make doubly sure if they want payment info up front.
3. Keep in mind that you may not see rooms avaiable online, but if you call and do not identify as a GenCon attendee they may actually have rooms. (I've always wondered what the motivation is for the hotels to NOT let you pay a higher price if you don't want to go through the housing process what with pretty much being gaurenteed to fill up. If there was more competition I would understand, but even Indy is getting tight for GenCon).
Oh, and as Sherilyn said, if you need an ADA room and are going through the housing process you need to need to actually call the housing group at the dates they will indicate for next year. As she did, if you're really concerned about it I'd try to get a room on your own first.