Switching with Pre-Arc, Then yes he would.Karin is just like Ino, but her healing is much more proficient and she is a sensory type. Compared to Jugo and Suigetsu, Karin was the most useful and the one who protected and heal Sasuke the most, and like CAG said, switch Karin with Sakura in the Kage summit and Sasuke would have died.
War arc Sakura with her seal > Karin's healing. Adding the fact sakura is a far better fighter, Monster strength, Being able to heal through her summon (meaning she doesn't even need to be close to sasuke to heal him).
War arc sakura would of been more useful to sasuke's Summit fight than karin in fighting/healing terms.