A police officer stopping a car cannot do so for the purposes of randomly breathtesting the driver.
A police officer can, at any time, stop any car for a documents check. If, while speaking to the driver, the police officer thinks the driver has been drinking, he can require the driver to undergo a roadside breath test. Not random, but because during the "chat" reasonable suspicion was raised, the officer can require a breathtest.
I can see the same applying to aircraft - if you happen to chat to a copper on your way through the airport and he thinks you've been drinking, hey presto - reasonable suspicion. Again, it's not random but the "Ways and Means Act" an be used to make it effectively so.