I'd been worried about that when I first tried it too. But it opens giant (130MB+) PDFs on my SD card just fine when in airplane mode and when I've had no cell signal. So despite the name, the Drive PDF Viewer app seems to run locally.
That's good to know, but still leaves me with the uneasy feeling of if/when this will change. For my taste, the cognitive load of all these security issues on mobile is a bit too high.
