I don't think it's about volume, weight is more likely, and I think it was mainly the Minuteman program that really required them. But I would suggest this was only a slight influence. People tried to build integrated circuits all through the 50s,and the first succesful ones  were somewhere around 1960. So there might have been a few years  when rocket programs were the main users,  between their development and first commercial use in the mid-60s.

Keep in mind that the big advantage of ICs, even those years, was the possibility to get prices down through mass production. Not really something the space program, or even Minuteman was very concerned about.