I'm going to offer a dissenting opinion.
If you are TRULY AND SURELY set on military/VA for life, I'd probably get it now. In the government world, MBA can be more of a check in the box requirement. For job advancement in the roles that I have in mind for you, they won't care where you got it from, just that you have it.
Outside of the public/defense sector, I would be strongly opposed to your proposition.
With that all said, if you think there is a chance that aren't...