The use of a rolling bookshelf is ballsy.
Where is the testing location? You'll want to ask someone who's tested there to see if its even a useful idea. You may need to contact the board to see if its legal. I don't remember the state specific testing rules being sent out until a few weeks before the exam, so this whole plan may be for nought anyway.
It passes the letter of the law in Maryland, as written a few years ago, if it fits under the table. If it fits it would only be in only one orientation though. I don't know how effective the set up would be in practice. The spines of the books would be out of sight, under a table, and pointed towards the aisle 90deg away from you. It doesn't make for easy access. I don't remember the rules for having to get up from your seat during the test.
I've heard a couple stories of engineers that brought in large bookshelves or boxes of books, setting up a mini-office around them. In none of those stories did I hear that the engineer passed the exam...