If Cork and Dublin play in a football or hurling match it's "Corcaigh agus Áth Cliath". I think the answer should definitely be accepted without the word Baile.
That's true that it is more common to hear Dublin referred to more commonly as a city but as you'll notice on emblems such as the GAA crest (which is on my profile picture), the combined county and city as a whole is just Áth Cliath.