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Yes. The Fan continues to operate thru settings 2 - max, but the aircon is only operates at 1, so on a warm day I am constantly flicking down to 1 to get that distinctive 'bite' an up again. I does blow cool air, but on a hot day its nowhere like conditioned air.
So in terms of the fist answer, yes I believe the fan is working - unless aircon and cool air have seperate fans.