but sparrows here is the object of a preposition, not the subject of the sentence

I disagree - that may be the gramatical analysis, but the analysis of meaning suggests that it is the sparrows under discussion and therefore central to any question that may have caused this strange utterance to be made: for example, "How many of the sparrows were killed?"

But I would return to the central point of style above all - it sounds awkward because it attempts to couple a precise mathematical term to the sentence in an unlikely syntax. The more natural way would surely be either to render the general sense with 'none', as you mention, or to put the precise term in its singular state by not jangling it with the plural noun: eg, "The number of sparrows killed was zero."