I had the previous Airport Extreme (the flat one) and I can use Time Machine backup by plugging my external HDD via the USB.
That is not a supported configuration. Lots of people report it works then is often flaky and when they go to retrieve data it does not work properly. I would not trust my backups to an unsupported setup.
https://support.apple.com/en-us/HT202784
From this link:
Time Machine can back up the data on your Mac to these backup disks:
- An external USB, Thunderbolt, or FireWire drive connected to your Mac
- An AirPort Time Capsule's built-in drive (any model)
- An external USB drive connected to an AirPort Time Capsule (any model) or AirPort Extreme (802.11ac model only)
- Network volumes connected using Apple File Protocol (AFP)