Absolutely! I have sat through several open book exams and not touched the books once :)
If you haven't studied for them, then your lack of knowledge will be apparent to the examiner as soon as they read your script. And why would you be sitting exams if you are not interested in the topic?
Only further study I did was work, which were 'closed book' of course, with minimum pass mark 85%. Never had any problems with those whatsoever.
Studied whilst in Army. Also studied AMEB Speech & Drama, to mid-20's.
Now informally 'study' varying interesting subjects through 'The Great Courses', on DVD.
I haven't had to wrote an openbook exam in ages but I would certainly study for the exam, openbook or not. I would however study differently, I would study where in the book each subject is located, instead of the answers to question. My goal would be to be able to find an answer quickly, and know that it's correct, instead of memorizing the answer alone.