Basically overwinding will make a pickup more powerful but darker.
Depending on the particular type of wire used in the coil, there's a limit on how overwound you can get (see Henk's thread on "true PAFs") - because the bobbin will be full up.
It's a question for Tim I think. An overwound Apache may, in effect, not be an Apache any more. Or it might work, but there might be something else in the range which will do what you want anyway.