I've used the transit system today in Stansted, and I spoke to the staff about the operation of the system.
Essentially, what
@Bletchleyite says used to be the case. For a period of time, passengers who accidentally ended up at Sat 1 or 2 were required to go through international arrivals and through security, as large signs were placed warning people not to take the transit system unless they were going to those gates. Then the system was changed, as it was causing a lot of unnecessary trouble for passengers. Now anyone who ends up at Sat 1 are told to go to Sat 2, where a member of staff will let them into the domestic part of Sat 2. From there, in the terminal, passengers with a boarding pass that is already 'airside' are allowed to simply walk back into the airside part of the terminal after being checked.
It apparently happens quite a lot, and the staff are used to it. There is nothing preventing/warning people not to use the system, so as long as you have time, I'd recommend taking a ride on it before it closes.
I also took a walk to the APV (90-93) gates, as I found some signs directing people in case the transit system is closed. If the transit system is closed, passengers to Sat 1 are directed towards the APV gates, where they board buses that take them to Sat 1. Those heading to Sat 2 are directed towards the walkway to Sat 2, where they can access the international gates which are normally only accessible via the transit train.