It's hard to say, since the QuickPlay web site doesn't offer much in terms of video specs. Can you open a QuickPlay video in G Spot or Media Info and note the resolution, frame rate and especially the audio and video codec these video files use?
That said, Premiere Elements doesn't output PDFs. (The Organizer will output a PDF slideshow, but that's not what you're asking about.) However, Premiere Elements can output a variety of video formats, some of which can be embedded into a PDF file using a PDF program.
So the short answer is no. There is no direct output as a video PDF from Premiere Elements.
But the long answer is ... Probably not. It depends on what you're trying to do and using what other programs to do it.