Did Gatsby take the blame for Myrtyle's death before Daisy rejected him?

Gatsby takes the blame before Daisy rejects him, and still holds on to it even after she does, still having hope she might come around again. On top of that, Tom covers up the truth further by telling Wilson Gatsby was Myrtle's killer and Wilson, in a fit of rage (believing Gatsby was the one Myrtle was having an affair with), proceeded to kill Gatsby.