During my 'Survival' Multiplayer game I created saves to be able to write a summary about the game, take screen shots, ect. If you've read my post, you'll understand. However, as I loaded up my various saves to take screen shots, I realized that the cooldowns on the Executive Orders were being set to zero when I loaded the game up. I wasn't certain, so I tested it. I loaded up my turn zero, drafted colonists, moved them 1 square to be easy to see, then saved the game, and re-loaded. Sure enough you can see the 'Draft Colonists' Executive Order is available again and its the same turn.
Here is the link to the base save (I've posted it in the Dev Journal #22 as well), and here is my post draft turn 0 save.
MP save - turn 0
MP save - Turn 0 post drafting colonists