Rules FAQ

Unopposed power is awarded in 4.2.3, but determining whether a challenge is unopposed or not is determined and "locked in" at the same time as you determine a winner (one step earlier at 4.2.2). That means that no matter what you do to your opponent's characters after winning the (opposed) challenge - including Throwing Axes at all of them - the challenge will still have been opposed when it mattered.

That isn't to say that Throwing Axe doesn't help you generate unopposed challenges - it is a powerful disincentive for your opponent to block. Furthermore, unlike in 1.0, if they do choose to block a military challenge with a chud, you can use the Throwing Axe to kill the chud, forcing them to choose someone else to die for claim.