I wanted to understand the supply system better, so I played the Austrians in the 1805 scenario. After they became unlocked I decided to put the entire army in ULM in the fort and simply let the AI do its thing. During the first few turns I noted that the stocks at ULM went down 134 points per turn. Given that ulm was unbesieged, this seemed about right. However, on turn 4 when the french moved in all of a sudden the amount of supply in Ulm increased from 200 to over 1000! To compound matters, my forces where able to remain fully supplied under siege until the end of the game.
Interestingly, after the game ended, I decided to take my one active corps and attack the besieging French. As expected, I lost the battle. However, then the french continued to attack on days 2-7 and my couple of elements of artillery managed to hold off the entire french army and my NM sky rocketed from 145 to 172. (See other post for more on this problem).