Assuming that funding is not an issue, is it within the limits of engineering to move Hoover Dam, including the Penstock Towers, in one piece a distance of several miles?
I would say no. Presumably you mean pick it up and move it in one piece. I can see how it would be possible to break it into pieces and move it piece by piece over a period of time, but I don't see how you could pick it up and move it whole. I calculate that it weighs ~10^13 kg. How would you lift it? And even if you could lift it, it would probably break into pieces under its own weight anyway.
Uh, given that you would want to tie it into the canyon floor and walls, it would make more sense to build a new dam and keep the old one as a silt catcher...
ps: I take it you'd empty the water before moving it ??