It does on my balcony where the fan pumps to, which has made doing any gardening difficult, but to the overall outside temperature it's just a drop in the ocean.
8 billion people running a 2000 watt AC continuously for 8 hours a day = 5 trillion watts of heat. (Only the electricity consumed by the AC is turned into new heat. The heat from inside the house would have moved outside anyway, at the same rate, since it's an equilibrium)
The sun = 175 quadrillion watts of heat.
So I would say, the heat from running ACs is not significant. It's also additive with all the other existing forms of energy use we have. Unlike greenhouse gases, which are multiplicative.
It is worth noting that if the Air Conditioner is powered by electricity that came from solar panels, the net heat produced compared to letting the sun heat solar panel colored ground is exactly 0.
Air Conditioners do not produce a net heating effect unless you power them by burning fossil fuels.
Not net zero exactly, since it’s a flows and rates problem, not static equilibrium. So it could even be strongly positive effect or negative effect based on how quickly the heat gets radiated back into space depending on how the wavelengths interact with the surroundings and the atmosphere.
Our current cities and infrastructure are designed to be black heat sinks to soak up heat and hold onto it and ground level. But there is research into what would happen if we flipped that design around.
When you enact 0.1% changes through a population, that's still a 0.1% change.
"If we all do this little thing" thinking is utter nonsense. If all of human consumption or contribution to warming or what-have-you is 1000, applying a change that lowers that to 999 is not doing anything more than that.
This here is not even a 0.1% thing. You could probably get a better result by telling people to read ebooks rather than hardback. It's just absurd.
Humans have a really hard time understanding compounding risk. But there are billions of us. How many billions of drops can you handwave away?