This will "work", assuming that you understand that you will have to log off of your current Wi-Fi Internet connection and manually log on to your "local" network.....and.....you don't mind being pestered with messages from AirPort Utility that the AirPort does not have an Internet connection.
Things would be simpler, and your backups would occur automatically if you simply connect the AirPort Extreme to your current network. Backups only occur over your local network.....not over the Internet.....so there is really very little to be gained by trying to set up a separate local network that requires you to manually log off of your normal network, log on to the local network to back up, then manually log off and log back on to your normal network.
Please understand that the AirPort Extreme uses an ancient USB 2.0 port, so backups are going to run at about half speed compared to newer USB designs. The USB port only supports a hard drive that is formatted in Mac OS Extended (Journaled), so you won't be able to use newer formats like APFS with the drive attached to the AirPort Extreme.