Most cameras check the time when it have acquired a GPS fix i think, so as long as it still remember your time zone you should be good.
But you risk getting a first recording saved by the default time date of the camera, so that will probably also be the first one to be deleted if the memory card are full as the default time/date always seem to be before present time.
I would advise you to inspect the memory card after a little while just to be sure, but normally dashcams get a GPS fix within a minute or so ( cold boot ) so if you use the normal 3 minute files, time should be correct before the first file are ready to be saved.