The ship surely exists in this time so the asset could be used however the fleet museum as we saw it in PIC definitely did not so its asset could not. Canon is that it is the original Spacedock that was towed to its current location and converted into a museum. Problem is - where would they find an NX-01 at this time period? All the way back at Earth maybe? In the VOY finale, I believe, they said that Voyager was a museum piece in San Francisco but in the new timeline its at the museum we saw so maybe the ships were originally stored there on Earth or in orbit (or maybe over the ocean, I guess since SF doesn’t really have space for whole starships to just sit around?) but were moved to the new location later (Athen Prime, if memory serves). I believe in “Relics” from TNG, it’s said that a Constitution class was a museum in San Francisco so I guess that would add to it.

I read in a thread and heard on a podcast people saying they were worried that we would revisit the museum again and I shouted at the radio in my car “It doesn’t exist yet!”