"you need to get the channel code of what you want to overlay and merge it into your existing main app to display on top of it's regular screens"
Short answer, no, sorry. Basically you would have to work directly with other channel authors and convince them to update their channels with a bunch of new code, and each case would be unique and a lot of work and testing and no one is going to do that. But you're free to try.
You can create a sceensaver application.
But if a screensaver works can we assume that Roku probably has the ability to run two apps at the same time?