Does Battlestar Galactica just poof out of existence the very instant Fuel drops to 0?
The humans do not lose the moment a resource drops to zero. They only lose if a resource is zero at the end of a player's turn. 

From the base game rulebook:


  If at least one resource is depleted to 0 or less at the end of a player’s turn, the game immediately ends and the Cylon players win. This is the most common way for the Cylons to win. Note that it is possible for the human players to reach 0 of a resource type and then increase it during the same turn without losing the game.


I don't believe the expansions change this.