No. The museum will be built atop its first exibit: tranquility base. See Futurama s01e02.

For the sake of correctness, Tranquility Base is not where the museum is built upon in Futurama S01E02; you must be misremembering. In fact, the moon landing site is considered lost at the beginning of that episode.

When it's later found in the episode, it's found with the lunar ascent module still attached. Because the astronauts ascended in this module, only the descent modules should be there, so you might at first think that this is a blatant mistake on the part of the writing staff and you might hope someone was fired for that blunder[1]. However, if you pay close attention, there's a plaque behind Leela while she's in the ascent module that states "Lander returned to this site by the Historical Stickler's Society."[2]

[1]: https://www.youtube.com/watch?v=FTxw5nQX7SA [2]: https://www.reddit.com/r/futurama/comments/91kssj/i_didnt_wa...

My bad. I do remember the issue re the assent module, and the sign, but forgot that they escaped into the lander after leaving the dome.

The book Artemis proposes this also.