Hi, I just received the answer to my questions from Axon technical support (thanks for that..).
Here it is:
Hi,
No the audio will not be routed through your network.
More complex answer: If Axon determines that the two parties cannot route directly to each other, it will insert a relay and route the audio through the Axon computer. In most cases this shouldn't happen.
2) Diverting the call automatically would go through your network yes. It will affect your bandwidth, but not by that much, because there is only SIP messaging data going through your network and no actual audio.