Possible, but you're only moving heat. You're locally cooling, but the net effect of AC is more heat. If a lot of that heat can get out of the atmosphere through radiation, then we'll start to cool the planet. Greenhouse gases make that difficult.
the net effect of AC is more heat
Yes, operating a fridge in your kitchen will heat up the kitchen. And yes, if that fridge is powered by burning coal somewhere, then it heats up the planet too.
But solar energy is already coming in the form of energy. It is not as if the sun is raining coal down on earth and we decide if we want to burn it or not.
I would think the amount of radiation given of by a solar powered AC will equal the amount of radiation it takes in.
It’s pretty clear that this is not the case.
Isn't part of that 'the law of conservation of energy'?
Solar panels are all black. So from a very nitpicky perspective, the energy used to power the A/C creates heat that is not radiated in the same way as, say, having a giant mirror on your roof would. The heat is also released locally rather than being aimed at the sky.
But from an overall perspective you are correct, because the alternative to solar is just having a regular roof which will convert some of the light into heat without doing any useful work, and because you'd probably get your energy from some less clean source.