Yes, it is. If I remember, basically, her brother gives her some time to get her bearings, then, yes, takes her home. Yoshida goes with and the brightest idea he has to make things right between Sayu and her mother who hates her is kowtowing and asking the woman to behave at least half-decently. He rejects Sayu trying to sleep with him one last time and returns home leaving her with her family.
Then in a while he sees Sayu at the spot where he met her originally, and it's strongly implied they start living together.
"then in a while" does that mean a time skip?