Changing the date does not affect am/pm.

Edit to add: if you do just change the date, check with your manual for what times it is safe to do this at - you can damage the mechanism if you change the date when the date wheel is engaged. On most mechanical watches the danger zone is within 21:00 to 03:00 but this varies so please do check.

This might not apply to all movements, but generally the hands indicate 12hr time in relationship to a 24hr basis that’s connected to the date indicator. Meaning, if you have the watch set to 6pm on one day, then quick-set the date to the next, it will indicate 6pm on that next day.