Here is a quick clue as to whether a 12V appliance will work or not:
A Mr. Coffee "plain Jane" 120v model consumes 850 watts. At 120v that is just a few amps ( about 7A ), and you can use "smallish" wire, about 18 to 16 ga. ( ie: zip cord, lamp cord ).
Remember that it takes the same wattage to heat water, regardless of the voltage, so if you cut the voltage 10x then the amperage goes up 10x, to 70A at 12v. Wire size is determined by current, so you need a much larger power cord. In this case, 2/0 or so ( about the size of your finger! For -each- wire ). So if that coffee maker ( or other 12v high power appliance ) does not have two "fire hoses directly connected to your battery via a short run, then it is very unlikely you will be receiving the same wattage as the 120v appliance. ie: most 12v kitchen appliances will not work at the same speed/power as your home appliances will.
In short: if that 12v appliance has the same size power cord as the 120v appliance, then it almost certainly will not work as well as the 120v appliance.
In the case of the 12v coffee maker, this is definitely the case.