Yes, CrossMgr will behave like the race ist still running after it is started - even if you turn off the computer and turn it on.
Pro tip (smart or lazy, you decide):
for p-2-p races, I often don't turn on the computer at all.
I just start the groups based on the time of day.
When I get to the finish line and set up the readers etc., I start the race, then do "Tools|Change Start Time" to set the start time back to the actual (earlier) start time.
You have to do this before any rider crosses the finish line.
This accomplishes the same thing as starting the race at the actual start time..
In this way, you don't have to be at the start if someone can reliably give you the start time.