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.
If your intern does work that you charge your client for, then of course it makes sense to compensate him or her.
At my unpaid internship, I came in with no programming experience. They basically paired me with sr. programmers so I could learn how to program efficiently, but was still too inexperienced to give me actual client work they could charge for. Believe me, I wouldn't want to charge the client either for the crap that I put out initially. But their investment will eventually pay off because when my skills strengthen enough to meet their standards, they'll hire me.
Our interns aren't "billable", but there's always plenty of work to be done to support the people doing billable work. Last year, one of our UIC interns wrote (in what I believe to be his first ever actual start-to-finish "program") a programmable symbolic process debugger for OS X, in Ruby:
http://bit.ly/13kxv3
Nobody paid us to do that, but that debugger work is now Ragweed, our house debugger, and we've got it working under Win32, Linux, and a couple embedded platforms. It's extremely useful. And we scored an excellent blog post out of it.
(Timur works for us full-time now, of course).
I don't have to compromise the work we deliver for our clients to put interns on useful projects. And we're a special case: we do hard core programming work on a billable basis. Most of the companies people talk about on HN don't have that problem. There's a million useful things an intern can do without jeopardizing product quality.
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.