My 2-ton 12 SEER heat pump outdoor unit draws about 6 to 8 amps at 240
volts when running. Start amps are about 20 to 25 amps. The indoor
unit draws about 2 amps at 240 volts. I use a window unit during power
outages, 120 volt, 1/2 ton. Then I can also run two refrigerators, a
microwave, the TV if the cable still works and some lights. I also run
a cord to each of two neighbors so they can run their refrigerators
too. If I ran my heat pump, it would reduce what Extra stuff I could
run.

What size is your AC? That would determine the answer. If it is much
over 3 tons, probably not.It depends on the surge rating of the
generator and if you have a hard start kit on your ac. My heat pump
has one, but I still prefer the window unit. Why strain an expensive
generator?

Stretch