Do punks and teddy boys get along?
John and Morrissey have little bits in common; love of girl groups; interest in the occult; love of cats and both great sense of humor. Lennon may actually have seems similarities in Morrissey to Paul. Both Gemini; both mercurical personalities. He would like him, but never turn his back on him.
John had a problem with Manchester and I'm not sure if it's a football rivalry thing or just some crappy experiences with auditions in the Beatles early days. I remember one fanzine stating that John HATED the Moody Blues for that reason alone. Morrissey at least was signed to DECCA. They were a 3rd rate label in John's day and perhaps even now. Any Beatle fans knows the story about what DECCA said about the Beatles.
Musically, John would have liked the Smiths. There are echos of three chord rock is some Smiths songs as well as 60s type McGuinn-guitar jangling. Morrissey's lyrics about England may have struck a chord with him. Lennon and Morrissey as solo artist have similiar writing styles; using just simple and blunt language to describe very complex emotions and ideas. I think John may have admired how Morrissey throws in words and ideas not usually covered in "pop" songs.
However, both men are of different eras. John generally was a positive person and a bit of an idealist. Morrissey is a realist. May not have made great music together, but perhaps have made a great situation comedy.