Gardiner struggled, but I don't think it was the "system", his skating, which is his strength was terrible early on. Due to injury recovery or age? no idea but he looked better at the end of the season before play was halted. Not sure what you mean by Skjei though. He played 7 total games without any training camp.. Hard to get any read off of that.
IIRC, Edmundson was health scratched a few times in St. Louis's cup run as well so inconsistency wasn't just a Carolina thing.
That said, Carolina's style does require strong skaters that make decisions quickly and can pivot quickly with lateral movement so Edmundson might not be ideal for it.
He was ok in Carolina, just not a guy I would pay much for. He had a few stretches of good play and was more physical than most of the Canes defensemen, but was really inconsistent and took a lot of penalties, at seemingly bad times. I think that's because he's not fleet of foot enough to keep up with guys. He's not that slow, but he doesn't have great quickness either.
If the Habs can get him at a decent price and term, they should be happy. If it ends up being $4M+ or 4+ years, I think they'll eventually regret that deal.