It is effectively the same as getting a shot at the doctor's office. Brief pain in exchange for immunity to disease. It is the same concept here. Brief pain in exchange for something that could have both practical and battle applications, especially if she gets something like Kamui which would be useful even in the real life of a normal civilian. Remember, right after the genjutsu, Sasuke would reveal that it was only an illusion. Therefore, the pain would be brief and nobody would be dead.
No, Sasuke fainted after the genjutsu. When he woke up, he awakened sharingan. Even if I turn out to be wrong about this, things probably work differently before you actually awaken standard sharingan. The bottom line is this:
Sarada would still feel the pain, which would make that special chakara in the brain activate, and she could possibly awaken something.