“Should I wait until the air conditioner gets turned on to tune my piano?”
The corollary would be waiting until you turn the heat on. Both reflect the futility of trying to time the tuning of your piano to some magical point in the seasons. The question does swerve toward the truth in recognizing that climate and environment have an impact on tuning.
There have been many studies done looking at the impact of various climatic and environmental changes upon the tuning of a piano. From my own experience I can tell you that tuning a piano for a concert without the hot stage lights on for an hour is a futile effort. As soon as the lights come on the radiant heat will quickly knock the piano out of tune. The heat is not affecting the moisture content of the wood in the soundboard as much as heating and thus lowering the tension of the strings. The soundboard will dry out some but this is a much slower process than heating the strings and harp.
If your piano is placed in the direct path of your HAVC air flow, especially if it is the air delivery vents, then every time your furnace or air conditioner comes on you will drive your piano out of tune.
It is not so much that a particular part of your climate control system is running, it is all a matter of stability. If you keep your piano out of direct sun light, and minimize the presence of sun light in the room itself, keep air movement across the instrument to a minimum, and maintain a constant humidity and temperature, your tuning will remain relatively stable.
However, one of my primary rules for the care and feeding of your piano is that you enjoy it! If that means putting in front of the window and playing with the sun in your eyes and the window open because that is what you enjoy, then by all means DO IT!! Enjoy your piano, we can fix everything else!