denver80260
The Short answer is YES!! The BTU's make no difference in the electrical scheme of things. What is important is how many watts of power the A/C unit will draw. If your 500 watts is the correct amount you will have more than enough power to run it from your generator.

Sister M
You are describing a 800 watt generator, not a 1250 watt one. The peak rating is peak, not running wattage. While the wattage is in the range, I'm concerned about the quality of the power. Home generators are a far cry from a high end commercial one. The quality of the power is not nearly as good as from the power company or a commercial unit. Motors are a bit picky on their power so you may have problems. Air conditioners cycle the compressor on and off which makes it even more difficult to regulate the voltage and quality of the power.