Excellent question.... and this was asked by Stephen Colley in a recent Google+ post
I know that you can use Micro$oft Word to convert the PDF to a Word doc, then change the background then re-save as a pdf but this requires Word. If you convert the pdf to a Google Doc then all you have is an "image" of the pdf and changing the page color does no good.
So, I went to my trusty pdf editor known as PDFEscape and I found out something very interesting... I can open the PDF, add a rectangle over the whole page, set its color and, wait for it..... change it's opacity!! I found that if the PDF was on a white page then an opacity of 30% makes it look great! I then took it an extra step and tried it with an image, and guess what.... it works!! Here is a link to a the pdf that I edited (note that it will show up in PDFEscape's read only viewer) Change the PDF background
My only compliant with PDFEscape is that it is not connected to Google Drive (at least as far as I can tell) so you have to do a "download - upload" dance. But for me, it is worth it!!
Let me know what you use to edit PDFs or if you have a better way of changing the background of a PDF.