Tanev doesn't move the needle in the slightest. The core can't score when it matters, Tanev doesn't do shit with that. Berube is just a meathead. I'd take Dean Evason over him. Hate that hire.
We’ll see what they do once JT and Marner’s money comes off the books next summer. If they don’t re-sign Marner and use his money to balance out the roster I can see them winning the cup. If they re-sign Marner, then no.
With players like Tanev, OEL, and Stolarz they're marginally more likely to not be in that position where they need that late goal. Although they won, what, one playoff round recently, they faced some decent to good playoff opposition (Tampa Bay, Florida, Boston).
The Leafs could catch lightning in a bottle in the next season or so with their current core, or they win sans Marner like you said, or they could win down the road closer to the 10 year mark from now. All of these are possible. There are always players that want to play for the Maple Leafs because of all the players from Ontario, etc. There is also prestige for playing for a big market that is appealing for some players.