Dear Ryan,
the simple answer is no. I don't know what minimum permsissions are required. The installation procedure, having to work on XP, Vista, 7, and the various servers doesn't handle/create/modify the users, their rights and permissions.
But once the installation is finished you can create a user with the desired rights and permissions, assign the AOLServer process(es) to this user and assign also to this user the folder C:\aolserver.
Having to do that I would replicate the rights and permissions of the user(s) created for IIS and I would treat C:\aolserver the same way the folder C:\inetpub is.
Hope it helps,
Maurizio