I understand where you are coming from and suing might be a little extreme, but honestly the school should work with him and not against him. Depression comes in many forms and isn't something that goes away. It requires a lot of work and the school needs to help him out. Expelling him won't solve anything and honestly makes it seem like depression is something to be ashamed of.
As well allowing students to vote on his future is just adding insult to injury. He doesn't need to have the kinda pressure on him and nor do the rest of the students, all that does is create an unhealthy learning environmental for everyone.
I do like your idea of extending his school year to help though, that's something the school should do instead of throwing him out.
I would only advise suing the school for unethical treatment if they refuse to co-operate after further inquiries, the current "deal" is retarded and has no chances of working, but first and foremost, the kid himself should acknowledge that the fact that he's not feeling up to something doesn't mean that he doesn't have to do it. People gotta do a whole lot of stuff even though they don't want to because that's how life works.
I understand that he's depressed, I fully acknowledge his condition and I experienced first-hand how such a person may act, but at the same time I believe that encouragement can work wonders. Excuse me for generalizing now but a great majority of the so-called "Depressed Teens" are depressed for superficial reasons and really need to snap out of it if they're going to succeed in life and go places.
If he *wants* to carry on learning, if he desires to get a diploma then he's entitled to do so - it's his civil right and the board of teachers has f*ck all to say in that matter, if they will deny him this right then hell yes he should sue, but only after he acknowledges his own faults and talks with the teachers personally.
Mixing personal life and professional life is a big no-no, the two have very little to do with eachother. If he was feeling really down and couldn't stand making assignments on his own, it would appear that he has a group of friends - each and every one of them could've helped him through it, and if not them, the teachers could.
Simple rules of school? Have paper slips for every absence, hand in assignments before the deadline and in the case of handing them late, apologize and give a genuine reason as to why you're late. If you just screw everything and remark "I didn't do *insert activity* because I've got problems" then it's just not going to work. I have problems, the teachers have problems. Quoting Gordon Ramsay, "Problem, problem, problem. Everyone has problems". That really doesn't matter, it's not a good enough reason.