With this hack it doesn't look like it.
The way I can see this works is your just plug the Axon into your computer via USB cable. From there you wire up the TX/RX line directly to your 2x3 programming header.
Unfortunately, I don't own an Axon, otherwise I'd try it out.
You don't need a usb-ttl cable because I believe the Axon has a ft232rl already.