What's the issue with testing someone without prep, then giving them a week to study up, and then testing them again? People take SAT multiple times, you know, and it is a brand new set of questions every time.
I did that myself (took it 3 times total), and I can say this: taking it without prep and then taking it later with just a week of studying on my own for about an hour per day made a massive difference. Even before I got my results back on the second try, I already felt i did much better, as I was second guessing much less and felt more confident about my answers. And the final scores reflected that really well.
However, studying beyond that (which I did for my third attempt, months later) didn't help much and just marginally changed my scores by +-20 in different categories (out of 700 total max in each of the three categories, which is how it was scored at the time). I didnt feel any more prepared either. Judging by my acquaintances, it was a similar pattern. Massive boost in scores on the second try, marginal or non-existent in scores on attempts beyond the 2nd.
For this to be a real test, you'll need parents of twins willing to send only one kid to test prep..and not send the other one..you know..for science. Doubt there is a parent who would do that.