By my understanding it should not - the gun is still treated as being moving during your opponents turn.
From a tactical perspective, it is usually desirable to unload your towed guns in a hex that is at the time not visible to enemy. This allows them to then get ready to fire the moment enemy shows up - not to mention that they will probably be able to get a couple of shots before the enemy spots them and returns fire.
The entire turn is only a couple of minutes so they only have that amount of time to unload & get it into position. The game is very kind to the larger guns which took a lot longer to set up & could not fire at all while limbered.
First question easy to check - move one and look at its "shots" at the bottom of the screen (it depends on the gun, how far it is moved, experience, suppression, etc.).