Apparently, not all models of the S100 are the same, as Dave on AUSPICIOUS had noted... They are designed to 'go to sleep' after a period of time, but mine will only do so when the AP is in STANDBY mode, otherwise it remains on as long as the main unit is on AUTO... The only way I can turn mine off without hand steering for a few minutes, and waiting for it to turn itself off, is to remove the batteries... A real flaw in design, IMHO, but mine is a much older unit than yours, perhaps Raymarine has since worked out those issues...
OK, I just got done with a nice little evening sail. I did a couple of tests with my S100 remote. Mine is a recent vintage, purchased last November. I do not know the firmware version.
With the autopilot engaged and S100 on, I pulled out a battery to kill the remote. My autopilot (Raymarine ST4000+ wheel pilot) continued to operate. It did not go into standby.
I then reinserted the battery and pressed the standby button of the S100 to turn it back on. The remote searched for the network and initially did not find it, giving an error message and saying "No Pilot." But after a few more seconds, it did engage with the network and the display said "Pilot." This means that the remote woke up and (eventually) locked in with the autopilot without taking it into standby mode.
So it would appear that my remote can both go dead and turn back on without affecting the state of the autopilot. Like you said, this might be affected by the vintage of the S100 device. It also might be a function of the model of autopilot that the S100 is connected to.
I was not able to verify whether my S100 goes to sleep while the autopilot is engaged. It did go to sleep at one point, but I had put the AP into standby and manually steered before I noticed whether the S100 was awake or asleep.