I would normally say no but seem to recall someone being DFA'ed while injured. Or maybe that was just outrighted.
I don't think they are really ready to do that though. Flawed as he is, he's still a more proven quantity than either of our current CFs. And just has more value than a bottom-of-the-roster pitcher or back-up AAA catcher (especially since they already have another one of those, though they need Marchan back first).
I also think he can reject the AAA assignment if he did clear. But you're not wrong that he might not get claimed or even be eagerly welcome as a free agent.