Reading the posts up to this point I think that there ias some talking at cross purposes. There is air con, aka climate control and an 'air chiller' which is always working when switched on.
My mk2 Zafira has the latter (SWMBO would have liked climate control but I was not prepared to pay +£K for just that feature - others were obviously included). It is effective in summer when needed an in winter to help th demist the screen. When on it continues to cool the incoming air whatever the cabin temperature.
On the topic of incresed fuel consumption there must be a hit which I can't quantify but if I switch it on when the engine is idling, the reva drop momentarily until the ecu festores them to idle, presumably by feeding in more fuel thus having the effect of increasing fuel consumption.
Malcolm