My test results from overnight are in.
I have exact same JSCH running in 2 different TEST environments (TEST1, TEST2) each with 1 single daily Job.
I Added a second Task to JSCH on TEST1 yesterday and used the transport case to upload to TEST2
When I check TEST1 today, I can see that the 2nd Task I added will run later today.
When I check the Monitor of my JSCH on TEST2 I only see 1 Task.
So, it looks like if you use transport case to update a JSCH, you either have to stop/start the schedule or use the "Reload Definition" option.
Now that I know this, I can let the users know.