Electric element turned on.......element will be burnt out due to lack of water
Propane turn on.......OK as far as propane burner BUT
What brand of water heater?
Atwood..........probably OK as tank is aluminum and t-stat would shut down when temp was reached. Tank can take the temp as long as it is allowed to cool before filling with water
Suburban......Maybe? Tank is steel but is glass lined. T-stat would shut down when temp was reached but glass lining may have cracked from the direct heating.
Fill it.......run it then if heats OK drain it and check for any 'debris' if Suburban