When I was a teenager (that is, when I was young and stupid instead of just stupid), I took a water-filled, two quart dish and ran household current through it with the aid of a couple alligator clips clamped to a stripped extension cord. I was trying to collect enough hydrogen from the process to make a nice loud pop and found that my DC supplies simply weren't sufficient. And yes, I know as I knew then that I wasn't just collecting hydrogen ... pure chemistry wasn't the point; the pop was. Within an hour or two, the temperature of the water had gone up considerably, and the terminals in the water had corroded. That water was too hot to touch.
Based on this, I think it's safe to say you could certainly cook an egg in such a set up. But it's much, much easier to just use home-made thermite. But that's another post.
