They had no connection with Manchester...
In Dublin at that time. Civil War. etc
And I understand John may have left home on bad terms
So a trip to Manchester Reg Office in
April 1922. With first son born 15 Dec 1922. All seems to tally
The wedding may have been at a Catholic church in Manchester. The words "Manchester Registry Office or Registrar Attended" in the marriage index on Lancashire BMD, posted by Ladyhawk (reply 7) means that either the marriage was at a registry office or a registrar went to attend the wedding at a church which wasn't Church of England. Catholic priests and Non-Conformist ministers in England weren't automatically wedding registrars like C. of E. clergy were. A Catholic wedding ceremony was only legally valid if a registrar was in attendance to witness it and oversee the register signing. Catholic clergy were allowed to apply to become marriage registrars from late 19th or early 20th centuries but they were slow to take it up.
John or Annie may have had relatives or friends in Manchester or they may have gone there for work.
My own Irish family went back & forth across the Irish Sea, between Lancashire and Mayo c.1900, depending on work and family considerations, thanks to cheap & efficient rail and sea transport. They had babies in both countries.