No. Once the other person uses Save in Google Photos, those photos are effectively independent copies in their library rather than live-linked items. Changes you make later—such as correcting the date—generally won’t propagate to their saved versions. In practice, you don’t have control over metadata updates after someone has saved the shared image to their own account. If the corrected dates matter, the other account will likely need to remove those saved copies and re-save or manually edit them there.