I don't know if there is a connection but there have been Dillons in Belfast for a long time. The 1843 Belfast directory listed the following:
DILLON
William, Solicitor, Arthur St.
James, Hatter, Wesley Place
John, Publican, George's Lane
Thomas, Publican, Pound St.
Mrs, College St., South
Ann, 14 Falls Road
You might check later directories on the Lennon/Wylie web site.