You are correct in your assumptions of the way the system works. To
install the software on the server you must bring the system down, which
will cause the router to go down. The best time to do network maintenance
and upgrades on a large network or on a network that cannot be brought down
is at night or on the weekend.
If you back up a database file that is opened, you will not get a proper
backup. Any files that are open will not be saved. It is best to do this
after hours, also.
There are many backup programs that start at a specified time. That should
be the best solution.