It's an interesting idea, but your typical unemployed person is looking for a job so they can sell their hours in exchange for money. A service like this allows someone to buy additional hours through paying someone else to do tasks for them, which is the opposite of the trade an unemployed person wants to make. Or to put it another way: why would I pay someone else to apply for jobs on my behalf if I'm broke and I have lots of free time? The only people I could see making use of a service like this are people who are already employed and want to get an even better job.

I think resume prep services are a much better opportunity for both sides. As an employer, I have seen a lot of resumes that would impress me a lot more if a competent editor spent 10 minutes polishing them (I'm actually very surprised that this signal hasn't been corrupted yet). And on the other side I've done some resume polishing for friends in the past and they went from failing to succeeding in their job search. To make it work for broke unemployed people you might try offering a money back guarantee. There are editors who will work cheaply on fiverr.com that you could outsource the grammar checking to.