I don't know if Katerina will survive the end of season 4, but I'm pretty sure they will be together at least until she dies.
-Now that Katerina doesn't have anyone to run from anymore and that her days might be counted, she will become a much nicer person.
-Stefan will be developing a darker side due to the events of the summer with Silas and everything, so that will make him more drawn to Katerina who's in a way a less 'pure' version of Elena because of her personality and life experiences.
-Just like Silas and Qestsiyah both said, the Doppelgangers are always drawn towards each other.
-Katerina and Stefan were once in love and she has said that Stefan was always the one of the two brothers that she truly loved.
-Lots of Sterina scenes in the next two episodes and possibly in the episodes after those two as well.