After some research into the way that the YouTube app handles videos I had discovered that it would be possible to run arbitrary code.
It's a bit hard work because the code would have to be added to a video file using a custom encoder, which I don't have the time and energy to do.
However after searching through all of smealum's emails I've discovered a YouTube account with a video uploaded not that long ago.
It seems that this video does indeed cause the YouTube app to run arbitrary code however it is not useful without any other exploits.
I presume that the exploit will require playing this YouTube video while having an exploit readily installed on your SD card, though I have no evidence that this is the case and have not tested it with any existing exploits.
If anyone would like to do that testing the video will be here before smealum takes it down:
?v=dQw4w9WgXcQ