Yes you can take the test open book. There is a good reason why the test is open book. That reason is because the NFHS probably realizes that many officials even the state level ones will open up their rule book and read the rules just to confirm what they already have in their mind. I use the test every year to refresh my mind and make absolutly sure that I am on par with the written rules.
However MANY MANY coaches at the kids level have never even SEEN the rules book let alone read through it. And this leads to a lot of coaches getting upset and saying that some official "screwed" their kid, when that isn't really the case. When I started officiating I got a real quick wake up call as to how much I did not know when I coached the year before that. It was amazing to me how much you actually do have to know. And I wrestled for 11 years before I ever started coaching and then officiating.
So yes take the test open book, read through the whole rule book, and I think everyone will benefit from it.