I would think that most (indeed all?) of the 'innocent' travelling public would go for this. The key bit is the false positives. I would expect a considerable effort at testing the effectiveness of this arrangement to get the lessons learnt and make any possible refinements.
We should also test for fallibility (ie things getting through). I don't say that in order to prompt a furore over system weakness, but it would a) allow for an intelligent assessment of risk and b) provide an opportunity to narrow down the necessary action when a positive is sounded.
It is vital that this is done in a structured way, involving practitioners and members of the travelling public, as well as relevant security experts.
What cost would you put on this?
I might also add that, perversely, this could throw up some negative publicity - at least in the short-term. Delay is delay, in many people's minds, and the cause of it is often a lost detail. Those who perceive increased delay (and have not previously sufferred any problems with the security regime) might moan. Solve that with good publicity in advance.