would something like that run a Window AC Unit in the summer / during the day?
Yes, with enough battery and a large enough inverter. There are vids of people doing it, but you need massive panel and battery to make it run for more than a few minutes.
Ok, going back to this ancient thought....
From the testing I did yesterday with a 1000w inverter and 300Ah LiFePO4 battery, and measurements taken from a window A/C in the garage, this is def possible, well within the limits of the inverter and battery.
I ran a 750W load (heater) for 2.5 hours and depleted the battery by 50%. Using very rough numbers and roundoffs, and ignoring the 20-80% LiFePO4 SOC rule, the heater could have run for 5 hours. My A/C in the garage maxed out at 460W, so in theory it would run 1.6 times longer than the heater, or 8 hours with no recharge.
So, yes, you could run a window A/C all day and if supplemented with solar panels, have enough for overnight.
And yes.... I'm going to try it when it's warm enough to run the A/C.