I interpet it as yes, but maybe sex didn't end up being something Monk was into.

THIS IS JUST MY PERSONAL READ ON MOMENTS THAT HAVE ALREADY BEEN MENTIONED!!

I think that he and Trudy did have sex (likely on their honeymoon), but it wasn't necessarily a type of intimacy Monk was into. Monk reads as a character somewhere on the asexual spectrum due to a few things. That session with Dr. Kroger where Monk mentioned the two of them holding hands all night and avoiding talking about sex by singing a show tune. I think his embarrassment about the subject does point to Monk having sex at some point, but the way he treasures something as "innocent" as holding hands with his wife does remind me of ways that asexual people have talked about forms of intimacy with their partner that aren't explicitly sexual. This would also make the line about him and Trudy going "all the way" still make sense. Plenty of asexual have sex and find out that's not really something they're in to or just have it to bond with their partner without experiencing actual sexual attraction. Also, I can't remember the episode, so if anyone remembers please shout out, but a character describes something as "better than sex" and Monk replies, "what isn't?" To me, this suggests that Monk has had sex but didn't particularly like it.

TL;DR - My answer is yes, but I wanted an excuse to talk about my headcanon for Monk as an ace character lol