No, he took over Nellie's stacked team and made them BETTER. Specifically they started playing defense, which would be welcome in these parts. They were far more serioius customers under Avery's watch than they ever were under Nellie's.
He had 3 full seasons with the Mavericks. He took over near the end of the 2005 season. He initially got the team to play defense in 2006 (which anybody would seem better after Nelly), and they reached the finals and that was the end of the honeymoon. In 2007, they won 67 games in a weaker west, and got kicked in the first round by the Warriors. After that, the team starts to unravel. There's unrest, players disagree with his methods, Cuban is upset at some of his decisions, they regress to a 51 win season, and get destroyed by the Hornets 4-1 in the finals. 3 years.
Looking at the big picture, and not just one year, it's clear that he took what Nelly had built, and done something with it for his first year. He hasn't proven he can build a team from the lottery. He hasn't proven he can develop youth. He took a team that had won 58 games the season prior, got them to 60 wins and the finals, they lose in the finals, and it's all downhill from there. About half the coaches in the league could have done that, because any coach that takes over from Nelly gets better defensive play. Look at Doc Rivers. He was almost fired, had one of the worst teams in the game, but when he gets a stacked team, they are the best defensive ball club and win a finals, and he's suddenly a great coach.
After reading articles about Avery and some of the stuff that happened, I wouldn't want him in the same state unless he was coaching the Lakers. When one not only alienates players, but causes them to make ultimatums to the boss to be traded or have the coach dumped, you don't want that kind of guy holding the franchise's future in his hands. He hasn't proven anything yet. Reggie Theus is more experienced in rebuilding a lottery franchise than Avery.
Guys who have coached top teams should never be underestimated. It was the mistake made with Adelman -- people think its easy, but its not something that everybody can do. Avery's Mavs were the best the Mavs ever were. He deserved all the accolades. The legit question is if he is one of those coaches who is doomed to wear on his team. That would make him an appropriate choice for a team alreayd in the hunt looking for an extra kick, but not for a rebuilding team that would need him to last 4-5 years before you could get off a legit shot.
No, he didn't deserve the accolades in my viewpoint. He didn't have to do that much because the team was ready for a change at coach and it was already a contender. And the defensive improvement wasn't as great as people here are making it out to be. And he only lasted 3 years before players turned on him and he got fired.