Your talking likely. I'm talking possibly.
I agree with you that he almost certainly will sign first and then either be traded or not. However, considering that other GMs could talk contract with Overhardt they could have a tentative agreement, subject to the other team being able to arrange a trade. Not the most likely scenario but possible.
This is where I was going earlier. And instead of an offer sheet the Jets will match or losing more picks then preferred (especially from a team that isn't a lock for the playoffs) the 2 teams work out something trade wise that is more palatable to each side.
I still think Trouba ultimately signs long term with the Jets. I haven't seen anything other than a tough negotiation to suggest Trouba wants out.