No, air conditioning units generate heat (that is how they cool!) and do contribute to local warming. Without AC the house reaches equilibrium with outside. With AC the house is cooled and that heat has to go somewhere.
They don't generate heat in the sense that heat is generated from nothing. If the AC is being powered by solar, then the energy that is powering the heat pump has already hit the earth and has become part of that system. The energy that would otherwise have hit the roofing and been radiated is more focused around the radiators, but as soon as that dissipates into the air the difference to the local climate isn't any different.
If the roof was white and reflective then a lot more of that light would be reflected, but most roofing isn't.
Your logic isn't really compatible with the laws of thermodynamics.
loading story #48911873
Right, but assuming conservation of energy holds then the net should stay the same, right? Unless solar panels have lower albedo than the roof they’re sitting on (considering how many roofs are flat black tar that seems unlikely…)