That trade makes sense for both sides. Evans gets the chance to play at his natural position. While some of his skills are similar to Rose's, his ability to always be a threat when the ball is in his hands will take a lot of pressure off Rose when he's back, especially considering that we have no idea how long it'll take Rose to "get back to normal," if he's ever able to get there. Evans proved that he's deadly driving to the rim and can draw fouls in bunches. He reminds me a lot of Rose in the sense that if he's able to improve his outside shot, he could become almost impossible to stop on offense. He's also got great size for a two-guard and is an underrated defender. Think of how much he could improve if Thibs got a chance to work with him.
Noah's leadership and defense would definitely be missed, but since the Bulls are strong across the board defensively, I feel like Noah's voide could be filled by some combination of Asik/Gibson/whatever rookie we'd draft.
We could look to take Andre Drummond with the 5th pick and slide him into the void created by Noah leaving. This also means more time for Asik. Think of it this way -- if we sign him to a QO, it'll give us a chance to see what he can do with more time on the floor (AKA, can he develop any skills on offense?). If Asik flounders after receving more time, it's obvious that his value is simply that of a backup center.
My only concern about Drummond is that he relies so heavily on his athletic ability that he'll over-value it to some extent. Many young big men tend to be lazy and don't attempt to grasp the defensive concepts that help make their atheltic ability shine. I think having a defensive-minded coach can help that, but drafting big men in general scare me. Drummond might be the exception, though. The guy has a freakish body and his speed, rebounding, and shot blocking are all elite skills, but he never once came across as a 'leader' last year. He also takes plays off, and for a big man, that's scary.