Some pictures are borrowed from the site the KC-GIDE is presented. Some editing is applied to get the proper scale and orientation.
Some measurements are made to determine the available space. Assuming you are
looking at the main board, with the back on top, like:
North is up, east is right, etc. Head room is the distance between board and the case above it. The red line is approximately the location of the graphics card and modem card space.
Conclusion: A populated KC-GIDE board will not fit in a processor socket of an unmodified 4p GA.
Connecting it via a short cable is very well possible, as enough space is available nearby. Unless of course a graphics board is present. Then it could get crowded.