Can a Yongnuo YN-560 III work with a Hahnel Combi TF trigger on Nikon?

For triggering the flash remotely from the camera:

Only if you also have a Hahnel TF receiver attached to the hot foot of the YN560 III as well as a Hahnel TF transmitter attached to the camera's hot shoe. You'll only be able to tell the flash to fire. You will need to set the flash power and zoom head using the flash's own control panel.

The built-in radio receiver in the YN560 III is not compatible with the Hahnel TF radio protocol, and the Hahnel TF system is not compatible with the YN560/RF605/RF603 radio protocol.

If you want to use the built in radio receiver of the YN560 III, or if you want to control flash power and zoom of the remote flash from the camera, you need a transmitter that uses the YN560/RF605/RF603 protocol, such as the YN560-TX.

For triggering the camera remotely with the flash attached to the camera's hot shoe:

It will work, you just won't be able to place the receiver on the camera's hot shoe. The actual signal is communicated via a cable that plugs into the remote shutter release port. Some folks use velcro to attach such accessories to a camera body without tying up the hot shoe when communication via the hot shoe is not needed.