No, you are greatly assuming things. Teams aren't saved by home-town hero's in any sport, there is almost no solid example of this since The Rocket across any league. The closest is maybe Joe Mauer. The kid being local is a novelty, and those things quickly disappear. The Preds and Tampa didn't become viable because they got some superstar local kid, they became viable and successes because they started to consistently win.
I would say you are being ignorant of the Yotes and there fans if you think the main thing that will draw them is having a local kid. I think most would be drawn in by a winning team more than having Matthews. Plus, if they are going to break the bank to sign Matthews to a contract the Leafs can't match, its going to be pretty damn hard to be a winner unless they spend to the cap. As an Oilers fan, I'm sure you can see one player won't get you into the playoffs.
I asked this question in a thread 2 years ago, and here are the responses I got.
https://hfboards.mandatory.com/threads/has-a-local-kid-ever-saved-a-franchise.2075649/