well after a while, sasuke might be able to figure out the ten second difference in shinra tensei. he does amaterasu, nagato might use shinra tensei. sasuke can then use his speed to go behind him and cut off his head or something. if sasuke can do kirin, it might be over if nagato can absorb that fast
Sasuke still doesn't really have a way to stop Chibaku Tensei. It doesn't really matter how fast Nagato absorbs, even you throw a lot of water at a sponge it will still absorb it. And Nagato's absorbing jutsu can take in an infinite amount of chakra.
sasuke would destroy chibaku tensei with black flameing arrows...we still dont kno how good nagato is with genjutsu off that alone nagato might get killed.
Black flaming arrows wouldn't be strong enough. It took Itachi's strongest long range attack, Bee's TBB!!!, and Naruto's Rasenshuriken to destroy the Chibaku Tensei.
We don't really know how good Nagato is with genjutsu, but Sasuke isn't that good at them either. Rinnegan is the next thing after the EMS so he probably has some skill with Genjutsu.
And if Nagato gets too close to Sasuke he might suck out his soul.