Yes But Mission Creep/Tangle Threatens
NASA and the Air Force have always had a symbiotic, uneasy relationship.
In theory, NASA's all about furthering exploration and development of advanced technology that could be used for military or civilian purposes with the results available to all with international participation.
The USAF's focus is first and always keeping tabs on the world and power projection for US interests and pushed accordingly with a culture of secrecy.
If you're cynical, NASA got to be the blue-sky lab exploring bigger and better launch vehicles that may or may not be used by the Air Force to make sunshine happen across the globe and improve surveillance capabilities, that also got used for a series of propaganda stunts, Gemini, Apollo, et al.
I'm not discounting the planetary probes launched and the impact they've had in planetary science, but they've been the cheaper, less flashy way to collect data that didn't have a dedicated military purpose, and thus less funding, but they directly benefited from the military work in improving sensors and instruments as well as telemetry to transmit data vs being data sealed in a can for retrieval.
If it weren't for SDI, nobody in DC would've cared about the Space Shuttle except as a space truck to run the various ABM killsats into place, when it wasn't assembling a space station to serve various military and civilian purposes.
AFAIK the US didn't research FOBS, and the Soviets scrapped their program to comply with SALT II, so it wasn't to put offensive weaponry in place, but the Air Force would dearly like to have that capability if need be.
At any rate, NASA and the Air Force have different missions and reasons for being funded with lots of crossover. My thought is that NASA could serve as both blue-sky research group and merchant marine that could easily be detailed to military missions. Also, the Air Force could offer SAR and salvage assistance to crippled civilian spacecraft/crews, but that's assuming much more going on space. My 2c on the subject.