I agree with
Misanthropy. The breathalyzers in Aust require a hard blow to work - an indicator light tells the cop that you've blown hard enough. The puffing action you get from continuos circular breathing would never be enough to make it work.
Demonstration of circular breathing. This guy shows you how to play a didgeredoo, but note that he only uses the "circular breathing" between full breaths. To beat the machine you would need to circular-breath constantly to avoid using alcohol-laden air from your lungs. Two problems here:
1: Not enough airflow to give the machine a reading.
2: The required cheek-puffing action is a dead giveaway. Even dumb cops will realise you're trying something other than a proper blow.
Unless the breathalyzers in the US are considerably different than the ones in Aust, I don't believe this is going to work.