There's a local charity I donate to that does this, they've got I think 10 or 15 apartments they put people up in for 3 months, and offer them various forms of placement assistance while they're there. In the last annual report they had I believe a 95% success rate with people they checked in with a year later.

Unfortunately this is pretty selective evidence, but I know for a fact they don't exclude people on the basis of having mental illness or addiction problems, I've worked with them personally.