As I've said a few times, I highly doubt the bolded.
There might be a few specific cases a year that jump, but the vast majority of drafted players are going to want to fast-track getting their ELC/signing bonus and get to NHL training camps and preseason games. And most NHL teams are going to want to get their hands on the player and get them into training/development camps.
And a lot of guys are just going to have loyalty to the team/league they're in - they've been mentally committed to winning that championship, they'll have friends, billet families etc. they like and are familiar with and there is always a risk associated with a change.
Even with undrafted 2005s right now, there have been virtually zero commits for the 25-26 season (is Tulk the only one?) and most of those guys are going for the 26-27 after completing their overage CHL season.