We make coffee using an inverter a lot. A few things to note:
Our 10 cup coffee maker is 800W. If our 4 batteries (440AH) are not at least 73% full (12.5V), there is a chance that the inverter will alarm. This is because the voltage drop from such a large load causes the voltage to drop below 12V. If the pot is unplugged, it goes right back to 12.5V.
Our 1 cup coffee maker is 400W. We can use it down to 55% battery as the draw is not nearly as high.
The most efficient way to make coffee when on battery power when using a drip coffee maker is to heat the water on the stove and pour it through the coffee maker yourself. This requires no battery power and the end result is the same if you take the time to pour the water through slowly - at the speed of a drip coffee maker. We would never run a generator just to make coffee. If I don't want to listen to it first thing in the morning, I assume others don't either.