I would imagine that won't happen, he will knuckle down, get a payrise after Christmas and forget this ever happened. He's too professional and driven to let this affect him, he has records to chase down. In terms of his value to Spurs he's worth twice what is on the table, he's literally the only chance we have of CL football and the riches involved in that. Top 4 looks as close to a closed shop as it was after Leeds went down, Kane can score the goals to break in, if Kane goes you may as well throw away the key.
Maybe I'm the delusional one but respectfully I think you're view is like, the maximum optimism possible in all worlds. I don't say it's impossible but highly unlikely.
Speaking as an outsider ...
-> With Kane in the side recording record numbers last season Spurs finished ... 7th.
-> Current top 4 and Leicester have all strengthened. Arsenal have no European football and Arteta has finally sorted out their defence.
-> Kane was caught on camera saying "what's the point?" during a game at the end of last season. He openly gave up on Spurs winning trophies in the Neville interview and effectively just went on strike for a week. Apparently half your fanbase now hates him and Son has been publicly critical of him. Only those involved will know the truth of what this "gentleman's agreement" involved, but it's obvious from his actions that Kane feels aggrieved, even if he misunderstood what it meant.
So on balance I think there's a low chance of Spurs getting top 4 and a low chance that Kane stays productive and happy, whatever he says in public.