Would definitely be an interesting concept. Similar to what they have in Tipp, where they play these regional championships off before the county championship.
The City championship would look like
Glen
Barrs
Douglas
Rockies
Na Piarsaigh
Bishopstown
Blarney (Not enough teams for a Muskerry Championship)
East Cork Championship
Sars
Midleton
Erins Own
Carrigtwohill
Bride Rovers
Fr O Neills
Killeagh
Cloyne
North Cork Championship (Avondhu and Duhallow)
Kanturk
Ballyhea
Newtown
Charleville
Mallow
Fermoy
West Cork Championship (Carbery and Carrigdhoun)
Newcestown
Courcey Rovers
There would be a lack of clubs for a proper West Cork Championship unless you added Premier Intermediate clubs like Ballinhassig, Valleys and Bandon.
Would make for an exciting mini championship, however I never see this happening in Cork. The club championship is already too hectic with clubs participating in both codes.