SuperCJN. I do not have AC on my Jazz, but I did on my previous car, and it made no appreciable difference to fuel consumption, no detectable diminishing of performance, and the heater was perfectly capable of blasting out hot air with the AC on. Apart from a couple of early tankfuls, when I didn't use it to check its effect on mpg, it was on constantly for over 9 years.
What I do agree with is it can chill the windscreen. On a humid summers day, when the heater was turned off, condensation would form on the outside of the windscreen, just above the demist vents.