Can PRT track YouTube videos and show their Google rankings rather than their YouTube rankings?

Yes. Select Organic, Organic Local, Mobile or Videos tracking type, add the YouTube video URL and select "google.com" (or other) as the search engine.

You can also track videos in Google Videos search (Organic, Organic Local, Mobile), just select a Google Videos engine.

Selecting YouTube tracking type and "YouTube" in the search engine drop-down will simply track the YouTube URL on YouTube.