Switching the climate control off will cause the engine idle to drop slightly because it no longer has to drive the aircon compressor.  On an auto this has the effect of reducing the amount the car will "creep".

You will get the same effect if you press the "ECO" button on.  And, yes, with the climate control on but the ECO switched off, it will use more fuel.

Sorry mate, I've managed to muddy the water.

It's the air conditioning part of the climate control that uses more fuel and raises the idle.  So either putting it in ECO mode or switching the climate control off will drop the idle back down and save you fuel.  But, of course, you need the heating and ventilation on or you'll be frozen and have misted up windows.

So the ideal setting (in winter at least) is to have the climate control on and the ECO on.  That way you will get heat and save fuel.

One further thing...  you should turn the ECO mode off for about 30-40 minutes every other week to run the air conditioning or the refrigerant gas will slowly leak out.