I don't see how any computer that has logged off (not locked) or rebooted could have a program in RAM. Sure, when your computer boots up, many services will load and any programs that have shortcuts in the startup folder will load, but they will not compete with another AC in the process.
Best practice would dictate that a computer be logged off and not locked. You can debate over turning it off or not. Our staff simply logs off so that log on is much faster in the morning.
The whole theory of logging off is to insure that there are no programs running either fully or in the background that could be accessing the database while backups are running.