Are you actually going to be getting extra? I know after I pay rent and then utilities the actual amount I pay out is above when I make for BAH. It'd be cheaper for me to live on base and have them take all my BAH because all your utilities are included. You might want to think it out.
To answer your question, no, you can't be restricted to only live on base.
To answer your question, no, you can't be restricted to only live on base.