Yes and no. When we were there in Nov. 2003, my DS (then 2 weeks before 4 years old) went to the Club. I, too, thought it was quite dark when I first walked in. But, there were lots of lights -- they were just hidden behind trees and pirate ships and all that. So, I think it definitely would not show well on a video of any sort. There are no windows on the one side of the club because it's a passageway to the lab and other parts of the ship I believe. I think there were windows (must have been to the inside of the ship) in the room with the computers and dress-up stuff.
My DS (who was very afraid of the dark) never complained about it at all. He absolutely LOVED the club. Unfortunately, we were only on a 3 night, so he didn't get to do as much as he would have liked. You shouldn't have a problem -- but I do know what you mean! Have a great time!