Nagato Can't use Chibaku Tensei AND Absorb Chakra at the same time.
Even if he used The 6 Paths he wouldn't be able to use Chibaku tensei,because He has To Transfer All his chakra to the 1 Path (Deva Path) And He has To Bring the Deva PAth Real close to him, in order to use it.
Why do you think he ran to the tree where nagato was at,because he has to be close.
SO bringing Deva Path, close to the "real'' nagato IS Dangerous since Sasuke has sharinan and Would easily Spot him and Kill the real one.
So using the Six paths, would be kind of be a disadvantage When Fighting a "Sharingan User'' (Especially mangkeyou) Because You're not gonna be able to hide the real Nagato that well, since the Sharingan see's Chakra, and Nagato is a BIG chakra source, so he shouldn't be too hard to find