No, no, Kubrick hated shooting on location. All those Vietnam scenes in Full Metal Jacket..? Filmed right next to London.

Now, he did fake the moon landing, of course, that's why NASA gave him the lens he used to make every single frame in Barry Lyndon look like a period painting... but much like with the start of 2001 (also filmed in London), he wanted lots of location pictures for reference (he didn't want to go there, wherever it was, but he had no qualms whatsoever about sending other people), so he demanded NASA send astronauts to the moon anyway to take those pictures, and the official moon landing was faked using those pictures taken in the real one as reference.