No, it does not. It depends on a lot of factors: the volume of waste that’s left, the coverage of the bowl, the condition of drain pipes.
To get you ultimately confused, there is a partial flush feature that can be implemented in both 1.6 and 1.28-GPF toilets. Having it is better than not. But a 1.6-toilet with a dual flush uses just 1.1 G for a partial flush, and if you compare it to a 1.28 model with no dual flush, the larger one may sometimes be just as water-saving.