Yes, though there was a divergence later. For various strategic reasons you want your ICBMs to use solid rockets, so while the early manned rockets were liquid fueled ICBMs mated to capsules, money spent on ICBMs today probably doesn't do much for a civilian space program.

On the other hand, I doubt we spend much money upgrading our ICBMs. The technology is mature, and that's an area where "good enough" is, well, good enough.