Actually, you don't have to turn the page to activate the feature, it seems to be part of the shut-down process.
I just tried it: set the boot screen to current page, load up a book, then shut down.
Powered up to the same page.
And it fits in nicely with the PB360's fast bootup time, which is why I have it to autoshut-off rather than let it run until manual shut-off. So now we get (fake) instant-on and the best battery life the gadget can deliver.