The power does run down even if screen doesn't change. The screen itself takes no power to display static text, but the processor inside the device does keep running (though in a reduced consumption state). In most cases, battery goes flat after three to five weeks in standby mode.
As for PDFs, they indeed have improved their display in 505, but it works better for some PDFs than others. You can get a feel for it by downloading the latest eBook Library sofware from Sony and loading the PDFs in it: