Yes he might have went anyway. But according to one report I read, Stoke apparently turned to Neil, when a different target would have cost them too much in compensation.
That's one way a contract can work, but in the end you can't keep someone who doesn't want to be here.
Neill will make more money leaving for Stoke, but unless he does very well indeed there, promotion next season at the latest IMO, I think his behaviour will damage his reputation in the game in the longer term.
Barring him revealing information that he has been as pure as driven snow in this, he'll find it hard to get any club to trust him down the line.