I would definitely bring down the DB to do a backup.
Actually, you shouldn't have to "bring it down"..
A more convenient way to handle this would be to implement a method on the repositoryController, #backUpTo: targetFileDirectory, that closes, copies the files via Squeak's FileStream, then reoopens, all wrapped in a requestCritical: [], of course.
So, you can keep your web up but just notify there will be a pause for however long it takes for Squeak to copy the files.
How does that sound?