Could be something inside the starter causing the drain. I would say the issue is most likely starter. I would hold off on replacing the battery for now. Replacing the starter just might solve the battery drain problem.
I had almost 200k miles on my 05.
I was having intermittent no-crank/no-starts over the winter. I was really thinking it was an issue with the Passlock 2 sensor or a switch on the door latch telling the security system to prevent it from starting. I would go through a ritual of opening and closing the door, waiting 2 minutes and trying again. I must have looked funny to other people in the parking lots.
It always managed to start at some point, so I put dealing with it on back burner. I did not want to get into projects that involved working on the truck out in the bitter cold.
Then, in April complete no start. I had my Tech 2 scan tool and was able to determine battery voltage, ignition and park/neutral looked OK. Went with the starter replacement.
I had been thinking my issue was more complex and possibly involving the security system. It was not. The starter was my issue all along. My Tahoe has been starting all the time since.