No, according to the Church fathers John was released from Patmos. He returned to Ephesus where he took in Polycarp as an acolyte and eventually made him Bishop of Smyrna.
But you got to remember that John spent time on that island. It is where Revelation is written.
But you said John was able to get off that island?
I did some research this morning and to confirm it there is the remains of a shrine in Ephesus which has his tomb.