Only issue with giving an offer-sheet is that next summer, we have our own high-profile RFA to sign, who is also going to want big money... By giving Gaudreau/Kucherov an offer-sheet, we may not have the cap space to re-sign Galchenyuk, and it will also create bad blood with Tampa/Calgary who may try to pry Galchenyuk away with a massive offer-sheet of their own.
Not illogical. But Gaudreau isn't eligible for an offer sheet. Kucherov, however, is. I'd offer sheet Kucherov. Yzerman will be way too busy with next year'a free agents to go hard after Galchenyuk in a move for vengeance. He's got Johnson, Drouin, Palat, Bishop, and Filpula to worry about. If Yzerman matches for Kucherov, you corner him a bit with next year's crop of FA's and you can pry one away next off season.
Also, no one would be able to go hard after Galchenyuk if MB signs him during the year.
And finally, I'm sure Bergevin is game for offer sheeting. There was a report that said he was preparing to offer sheet Brandon Saad last off-season because he knew Chicago was too tight against the cap to match. However, before MB could make his move, Chicago traded him to Columbus. If that is true, that tells me Bergevin is game to do anything and everything.