It was quite usual for Catholics to be married in Manchester Cathedral in those days and these were recognised by the Established Church.
Also, I think it became quite the fashionable thing to do in early Manchester.
A marriage certificate would give you the Father's name of the bride and groom. The reference for this could be listed on the Lancashire Births, Marriages and Deaths, and may confirm for you the bride's name, unlike FBDM site where you have a choice!
Hope this helps,
Patk