Generators used in high altitudes

They will run, but with slightly less power.
We do camp at 5000' and did not notice performance loss.
Than when I took my boat to Lake Tahoe at 7000' I had to replace the propeller with one having lower pitch, or the engine would not push the boat in hydroplaning.
Inverter generators do have extra engine power to speed up when needed, so I don't think you are going to have any problems unless you go higher than 10k