You won't be able to deliver the image that the roku is outputting to the screen directly, however, if you created the channel, then you will probably have created the graphics as well, and you can deliver those, either from your webserver, or by adding some webserver functionality to your Roku channel. There is a webserver example in the SDK, so you could theoretically serve up images from your Roku directly to your mobile app, if the app is on the same network (or if you open a port in your firewall, you could serve it up anywhere).
I don't see any reason why you couldn't accomplish what you have discussed here - your remote could check if the channel is installed via the ECP, then launch the channel, then deliver your content lists as XML files to your device, and have your device retrieve the graphics based on links in your XML files, from the Roku.
- Joel