Do you really need to do the double-blind study, though? The median person cannot program at all, so using rnd() couldn't possibly have better than a 50% success rate (certainly lower; 50% is just a round number that I'm sure is larger than the number of programmers). Is Google doing worse than that? I kinda doubt it.
Yes. You can do it at each stage as well. And we are not talking about hiring a general employee but a CS or programmer. So employ rnd() after a resume screen. Google has already found that GPA and brain teasers had no positive effect. This is similar and it would be an interesting experiment.