No, and to think he does is completely ignoring the reality of the situation. The Leafs were willing to write off the Clarkson money as they realized that it was a massive mistake made by a prior regime (and he was a useless asset). This is much different than Babcock for a variety of reasons. Lou did not have this power.
No one, I'm not even sure Friisdahl has the power to for anything related to on-ice Hockey performance. Babcock is the highest paid person in the Leafs management, by a wide margin. So, if Dubas wanted to fire him, it would have to go to the board. On top of that, Shanahan would lose serious job security due to the fact he was the one who agreed to pay Babcock this type of money, which makes it quite unlikely Shanahan (even if he could) would unilaterally agree to give Dubas that type of power. Finally, it would go to the MLSE board and be decided on by the board. If Dubas can make a valid case on why, then he would get the approval, but at the same time, if Babs thought there were a serious issue with upper management there is the chance he has the political capital to overthrow Dubas and potentially Shanahan. There aren't many situations where the head coach makes significantly more than his two immediate superiors.
Either way, I don't see Dubas trying to remove Babcock and I don't see Babcock organizing a palace coup.
Now, in 4 years and Babcock looks to be worn out, he could fire him. But, when there is over 30 million left on Babcocks deal, and likely only 10 or so left on Dubas's, its going to be damn hard to win that battle without strong ammunition and the board agreeing with it.