Can't say I've ever heard of this before, but it's an intriguing idea. The Golden State Warriors of the NBA have begun their own 24-hour-a-day Internet radio station dealing with all things, well, Warriors. There are interviews with players, coaches, details on promotions, pressers, etc, along with music picked by the team.

Warriors fine-tuning their first-in-the-NBA Internet radio service 

I'm not sure what they do during the off season.

I doubt we'd ever see this here. Rogers wouldn't want to minimize The Fan with a Jays station, since they own both of them. The Leafs and Raptors here are co-owned Bell and Rogers properties, and any competitors might impact both 590 and TSN - and judging by the last book, the latter doesn't need any more reasons for people not to listen to them. I could see other teams outside of Toronto trying this, though. I doubt it costs very much to run.

Warriors Sound radio