I can say with 100% certainty that the joke only works on one level. LDS was just Kirk screwing up LSD. The entire movie ran on gags about how out of place the crew was in that era.
Yeah, I think you're right.
If it had been intended to work on that higher level, they would've had some follow through, with Gillian saying something like, "He's a Mormon?!!??!? I thought he was a Hari Krishna!"
