Eh, it depends. The Kinect has only about 1090 depth values between 30 cm and 10 meters. Most of the values are concentrated in the low range.
So yes, while at close depths you'll get a 2 mm resolution, at greater depths the discretization error becomes much higher.
Of course, the main problem is not so much the resolution, but the noise and the image size. At 1.5 meters it gets really hard to track a hand because you get very few samples with unpredictable (noisy) values. You also lose samples (or even worse, get wrong values) around the edges because of registration issues and shadows between the infrared camera and the projector (plus the registration and shadows to the RGB camera if you need the colors). And since fingers are relatively thin, edges are pretty much everywhere. Estimating five fingers under these conditions is pretty hard.