Much less so, in fact. If you look at some of the archival footage that's been on TV lately, you see most of the engineers doing calculations of orbital mechanics using pencil, paper and slide rule.
As to technological advances to come from the space program, don't get me started. The PC you are typing on, the smartphone you use to be in touch with the world 24/7 and the fact that many "major" surgeries from 30 years ago are now done on an outpatient basis are just a few things that are an outgrowth of manned space flight.
I'm not doubting that at all. I'm saying the voyage to the moon itself is a technological feat on its own. Those computers then is what Atari 2600 is to the Xbox One now.