On my Airport Extreme Base Station, after plugging a Hard Drive into the USB port, I'm not able to see the HD on the network for Time Machine to do backups.

After plugging the HD into the AP Base Station, TM appears not to be able to see it for continued backups to my MacBook Pro.

This is normal and expected. TM backs up to a HD connected directly to your Mac differently than it does to a network drive which is connected to the AirPort Extreme. TM backs up to a drive connected directly to your Mac to a folder named Backups.backupdb. But, TM backs up using a special type of container called a sparsebundle file when it backs up to a network drive.

The two different types of backups are not interchangeable

So you won't be able to "continue" backups to the existing back up file on the HD. You will have to start all over again with a new complete backup to the drive connected at the AirPort Extreme by choosing the drive destination in Time Machine Preferences.

Do I need to re-create the network on the AP Extreme with the HD attached during the network creation process?

No, but there are some other things that will need to be checked and considered. The first would be to make sure that the AirPort Extreme recognizes the drive when you check using AirPort Utility / Disk tab. If you don't see the drive in AirPort Utility, TM backups are not going to work until the drive is recognized.

The USB port on the AirPort is underpowered, so some drives that connect directly to your Mac (which has a high power USB port) will not work correctly when you connect them to the AirPort Extreme unless you use a powered USB hub. If the drive is recognized when you run the AirPort Utility / Disk tab check above, you probably will not need to use a powered USB hub.

Another factor that you might not be aware of, and that is that the USB port on the AirPort Extreme is a 10 year old USB 2.0 design that runs at about half the speed of a normal USB 2.0 port on a computer. So, backups are going to be S---L---O----W with a drive connected to the USB port on the AirPort Extreme.

Finally, we assume that you have the most recent "tall" or "tower" shaped version of the AirPort Extreme. The older "flat" or "square" versions do not officially support Time Machine backups to a drive connected to the USB port on the AirPort.

Ran out of edit time, but one more thing to consider:

Backups to a drive connected directly to your Mac are much more reliable than backups to a network drive, so we would not recommend that you attempt this unless you have another backup plan already in place.

Good plan to stick with what works well.