It's not that simple. You can find beagles running agility, too. It's not a matter of 'training', in every case, it's that dogs are individuals. You are trying to stack your deck in your favor to get a dog that will do what you want. That means you need to look at BREED TRAITS, where the odds are FOR, rather than against, you in favor. I have a rat terrier with no prey-drive, and who is incredibly reliable off leash. That's an exception, not the rule. If I wanted a good off leash dog, I wouldn't get a rat terrier puppy. I would get either a-) an adult dog who demonstrated the traits I wanted (What I did), or b-) a puppy of a breed who has generations of breeding behind it, that gear it toward being what I want.
No. Airdales are not exceptions. They are terriers on steroids. They've very big, very drivey, very independent dogs - AS A RULE. Could you get an exception? Yes. I wouldn't count on it. I'd get a breed that would as a rule do what you want. But it's your dog, and your plans. And a lot depends on how competitive you're planning on being, too.
Here, read this:
http://www.dogchannel.com/dog-magazines/popular-dogs/articletraining_for_agility.aspx And again: Your dog, your life. Get what you can live with, first and foremost. Just don't get a dog expecting it to be an exception to the rule. Especially the "King of Terriers" Which are as a rule, again, the terriest terriers to ever terrier.