I think you can certainly make an argument for military spending in terms of the side benefits associated with developing any complex technology, but I don't think the societal cost of increased militarization justifies military spending.
"Tell me, do you plan to report on the millions we've saved by advancing medical technology or kept from starvation with our intelli-crops? All those breakthroughs, military funding, honey." -- Tony Stark, Iron Man.
I agree with TheComedian that the drawbacks mitigate the benefits a lot, though. The thing about space exploration is that the drawbacks are purely speculative (alien regard, exoplanet contamination, etc.) and are a lot easier to dismiss.
He answered that after a fashion. Military spending has the potential to bring about many of the same scientific, engineering and medical discoveries, but at the cost of increasing the conflict driving many of the societal problems that they could solve (poverty and disease in war torn countries -- see Afghanistan in the 1980s, caught in the crossfire).
As an aside, I wonder if something so convincing could be written about military spending.