I've tried and it asks for "school name" which isn't any help for veterans or active duty personnel. Also Autodesk uses an outside agency who verify student/teacher/school administrator status. There is no option for military.
IF they roll it out then I'd be interested, I had the solidworks veterans offer but havent yet had the time to dig into it properly (didn't find it as intuitive as fusion 360)
In the UK we have a "defence discount card" operated by a private company on behalf of the govt, to get a card you have to be a veteran, serving or have some other very close tie to the military. You are required to submit proof you are actually serving or have served (record of service), small fee for the card and then you get access to an online and in person collection of discounts.
I'm sure other countries have something similar so this shouldn't be hard for companies to roll out and would engender quite a bit of goodwill on both sides of the atlantic.