He's on my Do Not Draft List.
Though Connelly does not have one "holy crap he's evil" incident like Mitch Miller, there are a litany of strikes against him in the character department. Multiple incidents of racism, multiple incidents of parents of teammates and opponents complaining about him, multiple accusations of bullying.
Even if we are willing to give him a pass of "he's young, he can learn" on everything, I think the IIHF world tourney sealed it. With Team USA up 4-2 to Canada in the Gold Medal game, Connelly basically tried to behead Ryder Ritchie with no direct provocation. On the ensuing 5-minute major, Canada scored 3 times and won the game. Looking at the USA bench as events unfolded, I am surprised Connelly made it out of that locker room in one piece.
I think Connelly is a character liability, and as such I would have felt bad ranking him ahead of anyone on this list. Do I think he is irredeemable? No, I hold out hope he can grow up and realize that his actions affect other people too and it's not just all about him and him alone. But until he proves this for a significant period of time, I'd say "let someone else take the chance".