Not overnight, but it will have an impact. The system will shut off interior lights after a period of time, but it will cost the battery a few amp-hours of capacity. Further harm can happen if the gate remains open on a vehicle not used for the next week (COVID). With the door open, many systems controlled by the Body ECU will never go into true quiescent powerdown state, and the typical 50-75 mA draw could be several times that. A damaged battery can result.
Your mother was right: Shut the darn door!