Yes many things that have been done with the role, like playing with the inflection in their voices and exaggerated walkin styles and such would be lost as funny if the character were a woman.
But I do think Edna could be played by a woman because I dont feel that this particular role needs to be all that funny for the show to work as a whole. That line "no im not her father" could easily be changed and not at all affect the flow of the story. What I cant see is Tracy being played by a man. I could see Motormouth as a man in drag instead of Edna-- if they wanted to keep that element in their somewhere, which they would likely want to do in order to stay as true to the movie as they can.
I guess i see what you mean about how edna being played as a woman wouldn't affect the show as a whole, but when you pin point it to individual characters, the character of edna would be the worst. It would loose everything that is appealing to it because there is nothing funny about the character. The fact that a man plays the role just makes the individual character funny. But i see what you mean.
"Why do we play with fire?-Why do we run our fingers through the flame?"