I doubt Detroit would care much about trading with the Twins for Fulmer. They would be giving up a guy that probably won't resign with them. Sure, they'd have to face him for the rest of the season, but they're out of contention, so that shouldn't matter much.
It's the Twins that might be warry. They'd probably have to give up a prospect that could come back to haunt them for 6 years. I personally think it's worth the risk.