Yes, of course you should watch Star Trek! That goes without saying, regardless of your interest in Lower Decks.

(But yes, Lower Decks does make a lot of in-joke references. I imagine it's still funny without them, but you'll be missing quite a bit.)

BTW, Lower Decks is only one of three(!) animated Star Trek series now (with the others being Star Trek The Animated Series from the '70s, and Prodigy). I've only seen the first episode of Prodigy, but I get the impression that it might be less self-referential and thus might be a better introduction. Also, everybody says it's really good.