You can find this answer in the DOW FAQ p.3:
Q. When is the game officially over?
A. Battles are over the instant one side captures the required number of medals as established in the Conditions of Victory
section of the scenario. Players do not get to finish their turn; they cannot do Armor Overrun or Take Ground.
Q. If you capture a multi-point objective at the end of the game, is it possible to get more than the needed medal count?
A. No. In a scenario where a set number of medals is listed as the Conditions of Victory, the game will end when the
Conditions of Victory number is achieved. Sorry, there is no gravy!
For further questions, look here, I know Jesse will appreciate it.