A few months ago, a guy from DePaul sent me an email and we got coffee. His "weekend" was during the normal work week, because of his shift job. He was looking for something to do during that off time. He had no work experience in our field. We picked him up. He's been excellent.

So your (somewhat strange) questions, broken down:

"Apply for and get a job" --- Check.

"Work however many hours they want" --- You need to make a commitment; you can't just come in Wednesday this week and Friday the next week. But if "however many hours you want" means "I'll give you days X, Y, and Z of every week", then, Check.

"Wouldn't be expected to produce work we could charge for" --- I have no idea what this even means. Who produces work for no reason at all? Of course we're going to want you to do real work.

"And still get paid" --- Check.