They'd ask for ID though, right?
So would the place that's hiring you.
My bank charges $5.00 to anyone who doesn't have an account there. I've heard them say that to people there before who were trying to cash a check. I would guess they'd still ask for ID though. The question is, what kind of ID will they accept? Call around to some banks in your area and ask them that question.
When I used to work under fake names, I almost always used check cashing places. They steal a small percent from you, but at least you don't have to pay taxes at the end of the year. It all works out. I would have a photocopy of my drivers license (fake, obviously) and I would claim that I'd recently lost my original. I'd say I had the photocopy because my employer had needed a photocopy of it when I got hired and I'd made an extra copy. I also used banks that the checks were from, if they were local. They would know that the check was good, so they'd just need some ID.
What you do, is use something like a photocopied ID to build up other kinds of ID. Like, use it to get a card at a video store. Now you have a second type of ID. Use those to get a library card. Make yourself a laminated college ID to back it all up. You could probably make a realistic-looking social security card. The more fake ID you carry around in your wallet, the more convincing you'll be. And the more IDs you acquire, the more you can get.