If your idle motor system is operating correctly it shouldn't drop at all. It may dip for a moment when the compressor clutch engages and then it should return to the original idle speed. The tach is not the most accurate indicator and it may not be reading correctly. Also remember when the clutch engages, if the cooling fans are not running then they also hit the electrical system hard and make the alternator that much harder to turn too. The whole electrical system experiences a voltage drop and the tach is sensitive to that and can read low just because of the low system voltage.
David Teitelbaum