Injury histories yes , as in the context of "is there some underlying issue".
Medical professionals don't go "He has had random injuries before, so he will have random injuries in the future" because they are bound by science and not feelings. Of course some slick negotiator can try to throw that in but a smart GM would just ignore such attempts to swindle. He's healthy now, he's a great player when healthy. Jackets can use him, if nobody offers enough to convince them to let go of him.
He did not quit on either team. He was actually surprised to get traded the first time, and this time he had asked for a trade because he needed a new start but he's still going to play for the team until the trade is found, if that's what it takes. He played his last game for Winnipeg and dominated it, then he was out with injury.
Yeah I kinda did ignore his time out with depression. If he wasn't healthy they would have kept him in the program, if he was depressed he wouldn't want to come back (he didn't want to play hockey when he entered the program). I certainly don't think that people who focus on their mental health are damaged goods, not for any PC reason but just life experience.