Will my old employer's promises about a raise still count once they're gone?

This turns on how concrete the promise actually was, much the same way a promised promotion does. A raise that was a genuine, finalized commitment — confirmed in writing, tied to a review date or condition that's already passed, or otherwise a settled term of your compensation — is a term of your employment that a new owner generally steps into along with everything else when your employment continues through the sale; it isn't wiped out just because new people are now signing off on payroll.

A raise that was more of an informal conversation, or something conditional on factors like company performance or budget approval that never actually materialized, is much easier for a new owner to legitimately decline to honour, since it wasn't a binding commitment from the old employer either. The strength of your position really does track the strength of the original promise, so gathering whatever documentation exists — an email, a signed letter, notes from a review referencing a specific number and date — matters a great deal.

Raise it directly and specifically with the new owner rather than assuming either that it's automatically guaranteed or that a change in ownership automatically erases it.