Somewhat. Usually living "off-campus" is more expensive than living "on-campus," which means you'll get a bigger budget allocation. The only exception that comes to mind is berkeley, where (I think) the reverse is true. If you mark off campus and end up doing the other, worse case they'll reduce your budget, if they bother to check. If the reverse were true, then you'd probably have to keep bothering the financial aid office to up to your budget and provide some sort of documentation proving that you do, in fact, live off campus.
Just because your budget is increased, though, doesn't necesssarily mean more free money. They might just up the loans. But at least you'll have money on hand in the event you need it for something.