Is it possible to create a Diazo theme that works with Plone that has a video background? Can anyone provide a link to an actual example site that does this?
you don't need a Diazo theme for this; collective.blueline is a package that includes some helper viewlets to easily insert code on the layout of your Plone.
after that you can use something like jQuery.videoBG.
Something like it that is done with a mosaic tile: https://www.fbi.gov/news/stories/report-from-thailand-part-4
In the end, you can put whatever you want in a diazo theme though--it's just html/css.