It's going to depend not only on the conditions at that point, but also what your idea of "do-able" is. There will be some snow, even if it turns out to be a really low snow year. If it ends up like normal, then there will be considerable snow, so you'd have to be comfortable traveling on steep, sometimes icy and crusty, snow, and route-finding when the trail is completely covered. If you plan it for late May, I'd say you should be prepared to either deal with a lot of snow or cancel/reschedule if need be. It may turn out to be a low snow year, but it may not.
I've done some nice backcountry skiing on parts of the TRT (Desolation) in may of previous years :-).