What airplane and navigation system are you talking about? Real airplane or some kind of flight simulator?
If the Present Position is incorrect when the INS is initialized, it will NOT "re-align" itself! It should be shut down and re-initialized with the correct Present Position.
Though the FMS or other navigation system MIGHT be capable of radio updating via GPS, DME, or other means, it will NOT "re-align" the INS! All it will do is put an appropriate correction into the position output. Depending on the navigation system, that correction may or may not persist after the updating is no longer available.