Partially. Its because he's a pretty average passer. He can carry the puck well and makes good passes when in transition. But pairing him with Alzner, who doesn't really manage the puck at all, was always a disaster waiting to happen. Its why, even if you view Alzner as a top-4 D-man (and I don't), he was never going to fit in that role in Montreal. He wasn't going to and didn't work with Petry and he's not going to work with Weber, since neither of them are great passers and Petry can't play his game and cover for Alzner without making mistakes.
Alzner looked ok for most of his tenure in Washington because they always had Carlson and one of Green/Niskanen on the roster when he was there. Plus elite forwards. Having two RHD at all times that can skate, pass and transition the puck well and dominant scorers will help a lot. Montreal has good RHD, but Weber doesn't carry the puck a ton and is a mediocre passer and Petry is a mediocre passer. And Montreal doesn't have the offense either.