Under the dome structure it's a giant hole in the ground. I like your idea, but I'm not sure how feasible it is given that fact. Also, any such park would be within the boundaries of Reliant Park, which would make access a little difficult.
I am well aware that the field of the Astrodome is twenty or thirty feet below the surrounding ground level but I feel quite certain that filling a hole with dirt would prove to be a solvable engineering challenge. I was thinking that the feasibility of the project would depend on factors such as the ones mentioned here, asbestos, cost, things like that. The idea that the Astrodome somehow plays a vital role in the delivery of electricity to Reliant Stadium is so fucking stupid that it just must be true.
As for the park, I've heard much discussion over the years about turning the ground that the Dome sits on into some sort of green space or another. Whether that will ever happen or not is another question, but I do know it has been discussed.