As a K-cup owner and coffee drinker, I think I understand your (his) concern.
Yes, the generator will easily be able to run the coffee maker.
Your generator can handle up to 4000 watts. All you need to do is simply "add up the wattage" of the appliances running. The Keurig is 1500 watts. The microwave is probably 1000 to 1200. The air conditioner is likely 1500. If an electric heater is running that's 500 to 1500 watts. Electric blankets are 200-300 watts.
Pick any two big wattage appliances to run at the same time at stay under 3000 watts.