?? No it wouldnt. The calipers dont require the power of the engine to spin them, they are stationary as the disc moves, so it wouldnt affect the unsprung weight at all. And as stated above, by making the drum brakes at the rear redundant, you can use a lighter material such as aluminium for the hat, so if anything you are reducing the unsprung weight.
EDIT: Oops my bad, im getting unsprung weight mixed up with the rotational mass components, ie, wheels, drive shafts, brake discs etc. But what are the cons of increasing the unsprung mass?? Doesnt it just come down to a trade off between bump absorbtion and vibration?? As above in my previous, wouldnt it actually still be beneficial to reduce the ROTATIONAL MASS in the system by using lighter materials for the brake disc composition (by no longer needing heavy hats for drum brakes)? This would negate any weight added by an extra caliper system, as well as minusing the weight of the existing drum brake setup. Of course, this only applies to a rear twin caliper setup.