If I had to guess: Yes and no. What I mean by that is that, like most Uchiha's, he probably can only "switch" back to his Sharingan after using too much chakra and not being able to maintain his Rinnegan any longer.
As to why Nagato couldn't switch back to Madara's Sharingan: Like Kakashi, he most likely just couldn't, or because they 1. weren't his eyes, and 2. he didn't have any knowledge of an other ocular form of his eyes; he probably thought that the only form his eyes could stay in was the Rinnegan.
Just my guess :/