This depends of the backup system you use, but in general it is a bad idea to modify the contents of a device while you're backing it up. However, you can read its contents; that's a safe operation, even if it will slow down the process.

What I do is not to use the HDD at all during a backup. This is the safer way to get a fast and consistent backup.

This depends of the backup system you use, but in general it is a bad idea to modify the contents of a device while you're backing it up. However, you can read its contents; that's a safe operation, even if it will slow down the process.

In your case, rsync will build up a file list and then start the backup. Therefore any file you add to the source HDD after the backup has started will not be copied.

What I do is not to use a device at all during a backup. This is the safer way to obtain a fast and consistent backup.