This is a great idea. Even if the publisher doesn't want to send the whole document to individual volunteers, they could send portions to groups of volunteers. That guards against a leak of the whole document.I have posted this so many times...
I have deluxe editions that cost me a lot of money that contain glaring typos, omissions, and errors. The vast majority of the mistakes I spotted on my first flick through. It is good to see that these days you release the pdfs early enough that the fanbase can error check before things go to print.
I suggest that you get volunteers to error check - they are not allowed to alter text or suggest that their bestest eva house rule is a better way to do things, all they have to do is spot the obvious errors, typos etc.
Then it goes to playtest.
Then beta pdf for general release to fix last minute mistakes before it goes to the printer.