I know that Rengar can see champs in the fog of war when his ultimate is active, but can he see the real Shaco when he ults as well?
Rengar's ability that you are talking about is called True Sight.
This ability causes stealthed units to become visible to the champion with true sight.
Shaco's hallucinate creates a clone which is classified as a decoy pet. Which is not one of the things that true sight will reveal so while Rengar's ultimate is active he cannot distinguish between the real shaco and his clone.
If Shaco uses his Deceive (Q) this will be revealed by true sight. Jack In The Box's Boxes will also be revealed by true sight.
There are many other ways to tell the difference between the two of them, one such method is simply by looking at the buffs, the clone will not get the red/blue buff if the real Shaco had it.