Kemet: Controlling another Player's pyramid and Victory point
Yes, a player who has a pyramid with no units on it in his home city automatically controls the pyramid.  

Here's some supporting threads from BGG.  Look at the second (italicized) line.

From BGG "Kemet Supplementary Rules"
(emphasis mine)


  Pyramids: A zero level pyramid means no pyramid is present. You control any pyramid in your city that is unoccupied. You control any
  pyramid in an enemy city where you are in sole occupation, and may
  upgrade it (getting its temporary VP) and/or use it to buy tiles of
  that color and teleport from it.


This is also backed up by the "City Control Question" thread.