I toured the Hoover Dam before 9/11. It is really impressive. Built in four years! Now, they take longer than that to pave a road.
It was also closed after 9/11. I don't think they ever reopened it for tours, not sure.
Yes, it is a popular spot.
And yes, I think you would die if you jumped off of it. If the fall didn't kill you, you would drown.