Sasuke might activate his Rinnegan, but like the Madara (pre-impure world) he won't be able to use it either. The Rinnegan drains the life force of the user. That's why Madara gave to Nagato who is an Uzumaki. Nagato died looked older than Jiraiya, who was a lot older.

Everyone to ever use the Rinnegan had a Senju/Uzumaki powerup:
--The Sage of Six Paths "evil" son inherited the eyes of the Sage but he still had the same DNA as his brother.
--Nagato is an Uzumaki. Shouldn't need to explain that one.
--Tobi/Obito is half Zetsu. Zetsu is made from Senju DNA
--Impure world Madara has the face of Hashirama Senju growing out of his shoulder.

Sasuke can possibly awaken the Rinnegan but he won't be able to use it without a Senju/Uzumaki powerup... Sorry