The mods can verify on a patching level, but I'd assume it should work. Adobe lets you use any account on at least two devices logged in simultaneously. The GenP guide only mentions the account should be in no way associated with any genuine Adobe subscriptions or your real identity/details. If you do encounter issues though, it's super easy to make and verify a brand new account for your new PC. And you'll have to patch the apps with the latest GenP version regardless after installing, no matter what account you use (again, as long as it's never been associated with any genuine subscriptions)