Primates are optimised to thrive on the primate-appropriate foods most abundant in their environment. Primates have also evolved behaviours which cause them to seek and avail themselves of scarce, higher value sources of nutrients wherever possible.

Whether primates graze all day long on leaves depends primarily on the type of primate and secondly on the types of food available. http://www.britannica.com/EBchecked/topic/476264/primate/51434/Diet has a good overview of the variety of diets primates have.

I believe it's clear that, yes, in an environment with small amounts of highly nutritious foods, creatures can eat less volume/devote less time to nutrition and still thrive.