[M_a_t_t]

First thought without too much thinking, yes. But maybe no.

When the voltage drops low it means the alternator can't supply enough power. This isn't the case when the a/c is running, but the a/c is not powered by the alternator. However if the fan and a/c consume roughly the same amount of power (mechanical via belt or electrical power) then the engine would/should be using the same amount of extra fuel to run. Since the a/c doesn't work it's impossible to test and be able to tell. Plus the a/c runs only part of the time so you would have to average the energy useage vs the constant draw from the fan.

TLDR:
Too many variables to say.