I don't think it is a huge deal, but it might matter a bit on the fringes.
I lived near Boston for a few years, and in Boston the attention, and crticism Red Sox players get is similar to what happens with the Leafs and the players in Toronto. Listening to sports radio, reading the articles, hearing what players said AFTER they left Boston, this is the conclusion I came to:
-Pay players enough money, and they will play for the Red Sox. BUT, you aren't getting any more players to go there or players any cheaper becasue they are good team or in a 'baseball crazed city'.
-There are some players who will not play in a city like that. They won't publicize that, but some guys, when their agent gets a call about an offer from a team with a crazed fanbase..those players often say 'lets see what else is out there first'
So what do I think that means for the Leafs? Overall not TOO much. They get the advantage of some guys later in their career coming here for less money for bottom 6 roles because they might want to play a year or two 'back home'.....but the negative is they likely have SOME guys (not too many) but SOME guys that quietly tell their agents they would rather go to 'worse' hockey markets where they and their family can go out to eat or the supermarket without all the attention rather than Toronto (or Montreal for that matter).
On Buffalo sports radio, Craig Rivet was a host for a few years and he described his time in Monteal. He said there were great things about it, but with all the attention it 'just wasn't for some players'. Same probably applies to Toronto.