Would this Google LVL policy implementation be reasonably secure?
In regards to piracy, there's always going to be a risk, nothing you do will prevent it completely.
As opposed to other risks, you risk upsetting your customers with an app they can't use.
I would expect a lot of 0* reviews from unhappy customers who can't even use an application they paid for as it's been disabled, whereas the people who got the app for free will likely have no interruptions. It's like buying a dvd and getting your face full of copyright warnings, when the pirates receive uninterrupted viewing.
I would insist on a licensed response when purchasing the app, and not bother with the second response. If someone can find their way around one response, they will find their away around the second.
Edit: I agree with kcoppock that a licensed check 20 minutes after purchasing would cause the least interference to customers and avoid the refund bug you've mentioned