The Jets traded their 1st last year but also had all intentions and tried their best to re-sign Stastny. I doubt that the Jets trade their 1st, and certainly not their 1st and Vesalainen for Duchene, a guy that they probably don't have a high chance of re-signing.
I would hope that if the 1st (or a good prospect) is in play, it's for a piece with term, or a player they think can fit for the medium / long term.
I said the Jets had intentions of resigning Stastny after they traded for him. By far the general consensus was he was purely acquired as short term piece, the Jets tried to get him to commit with a big big push. Obviously it didn't happen.
IMO the Jets viewed Stastny as a key piece to bolster their legitimate SC hopes. They paid what they had to because they felt he substantially improved the team and their chances for the Cup. Chevy said if Stastny had resigned there would have had to be"more surgery" to make him fit cap wise. They didn't do it blindly.
Stastny did do what hey hoped in any ways even though ultimately they did lose to Vegas. I forsee the Jets willing to part with at least similar assets to mirror that scenario. I have no doubt they would pay a premium price if they truly feel the player obtained tips the odds in their favour.
I doubt Duchene would be the guy due to the price, he most likely would only be a playoff player BUT he dramatically could improve the Jets chances and performance in the playoffs. I would not discount a move for a big name player ( Panarin Stone Duchene ) with only Stone viewed as a player to sign.
No one wants to part with young assets but a Cup win would be worth parting with a couple of top pieces, of the course the catch is that isn't all guaranteed. That is what Chevy will weigh and have decide on.