Guy Boucher is currently working alongside Sheldon Keefe as an assistant coach. His role with the Leafs right now is running the power play.
The Toronto Maple Leafs power play is 6th in the NHL, and credit to Boucher for his willingness to change things up when he sees that something isn't working. but with their personel, the Leafs should be ranked higher than 6th.
One has to wonder if Treliving's signing of Boucher was a backup plan for if he needed to fire Keefe. It's easier on the GM if your coach's replacement is already with the team. If Keefe is fired, Treliving could promote Boucher to head coach on an interim basis until the summer. See how he gets the Leafs to perform in the playoffs before making him the head coach long-term.
Although Boucher's coaching record of 191-186-46 is not as impressive looking like Keefe's, Boucher has coached a team beyond the second round of the NHL playoffs on two occasions. Helping this Leafs team get beyond the second round is job number one for any coach this season.
Another plus to making Boucher the new head coach is that he already knows the players. A new coach coming and not knowing the players is more of an adjustment than promoting from within. I think Boucher is Treliving's first option, but I also think Treliving will look at all of his available options.