I believe he actually did. I agree all of this film in general is based for interpretation, but check this perspective. The whole purpose of imagining Sophia was to have her as someone who, outside of his own mother, was supportive of him. Hell, even his own mother questioned him to be a comedian. So, every time she showed it, it was during a period where he was either felt empowered like after killing Wanye's employees or feeling vulnerable like when he was trying to do his stand-up and when she magically appeared at the hospital room with him. Once the truth was revealed about his mother and in turn the truth about himself, everything was shattered. It's why he came to her apartment FOR REAL and saw her as someone unlike whom he imagined which was always there supportive. The moment she said something about his mother, that's when it cut to the scene of him leaving. To me, I feel he DID kill her, because this also sets off the motivate to kill his own mother that next day. Also the sirens and the lights of the sirens came straight to that apartment and if you paid attention (I seen it twice), You hear a person banging at the door down the hall whole Arthur was chilling back at his apartment.