Even if you start Season and time runs out on you, that character will still exist, it will just get converted to non-season. So by all means, fire up a game with your friend.

I'm not totally sure how it works on console, but on PC you powerlevel by having the "levelee" host the game at the highest difficulty they can manage, and then the "leveler" will join that game and do all the murder for them. They'll get a ton of levels in a very short time.