Add drive to time capsule

Yes and No, if you are asking about Time Machine backups.

Yes, if you only want to back up the Mac that has the external drive attached.

No, if you want to back up to an external drive connected to another Mac

AMF in Atlanta wrote:

If my Time Capsule 2TB is full, can I still use the networkEd backup function via adding/connecting an external HD to the Time Capsule?

The external HD plugged into the TC does not extend its drive size... so it cannot use it as a single large drive array.

But you can can move a backup from the TC.. to the external drive.. it runs somewhat slower than the internal drive but that won't matter for wireless connection.

Once you have a new backup on the USB drive.. delete the sparsebundle of the backup on the internal drive of the TC.. that will then give you more space.

It is also possible to archive off the whole TC to USB drive.. and start new backups after you wipe the TC.. this is a better way to go imho. USB drives can sometimes be problematic with spin up and spin down continually.. and the computer simply stops being able to connect to it.

What model is your TC??

There is another approach.. on a Gen4 TC.. I would tend not to recommend it on a Gen5 due to its increased fragility.. you can put a 4TB disk in the unit. Since it will be out of warranty now.. a 4TB green drive like the WD.. will make a big improvement.