[dipso]

Patch it up. Use some fixall or plaster of paris first, then float the top with mud.
Mud alone at that depth would never dry. It is also easier to sand.

If it really bugs you you. Just cut it out and put a new piece in.
You can cut out a square or rectangular hole, Take a couple pieces of thin wood ( 1/2" x 1") span them across the hole you just cut, on the backside. Pull them tight against the wall and screw them in place from the outside with drywall screws.
Then take a new piece of drywall, precut to the size of the hole you made and then screw that to the 2 sticks with drywall screws.
Tape up the joints, mud, sand, fake texture and paint.

I wouldn't be to worried about just patching it up. Isn't the base going to cover most of it anyways?