But what if you don't use AirPlay?
Like I said, I have XBMC on my iPad, that provides streaming via UPnP (it works streaming to my computer). I can set up my iPad as a web server, etc... Would any of that allow a (albeit roundabout) way to play iPad content on Roku?
Roku doesn't support UPnP or DLNA. I could see possibly someone creating a Channel (Application) for Roku to do it. Roku doesn't support AVI container at all, so you'd need a transcoder of some sort in addition.
Roku primarily was designed to stream content from the Internet, not local devices on your network. Other options are to use a PC or MAC on your network and store the media there. Then you can use the Plex Media Server (which is similar, and a fork of XBMC) to stream your files to Roku.