No he won't.
He wasn't even all that good when Hitchcock coached there, and Hitchcock has a history of giving goalies career years. Cechmanek, Turek, Esche, all looked good under Hitchcock and looked poor elsewhere. Steve Mason looked like a future star in his rookie season under Hitchcock, then never looked good again until he changed scenery. Brian Elliott hasn't even had an average season yet without Hitchcock. Not before he played for Hitchcock, nor after.
And Jake Allen was a slightly above average backup/1b guy under Hitchcock.
I'm not defending Yeo by the way, just saying that Allen is likely nothing more than an average goalie at the very best.
Would the Blues be a top-10 team in the league with Quenneville/better coaching? Probably. They should be a top 10 teams in the league right now, but their goalie tandem just isn't good enough. If you take away their goalies, they easily have a top 10 roster in the league. But that doesn't mean the goalie would be top 10. Best case scenario is that he's a Martin Jones type that is a starting goalie on a really strong team, but not top 10 in the league.
By the way, in my little project I'm doing, Jake Allen has allowed the second most stoppable goals this year by my count. He's allowed 14, which is one behind Mike Smith. Braden Holtby and Cam Ward are giving him a run for his money right now and trail just behind him at 13. What do all these goalies have in common? None of them have a save percentage better than .900% (Holtby is at .900) on the season. I also have Craig Anderson at 13, but he's faced more shots than any of these other guys, if not more than anyone in the league and I bet he's probably even played more games this season than any other goalie in the league.