I'm curious to know how difficult it would be to add something that would allow the app to report back to an LMS.

Unless the LMS provides some sort of API other than SCORM, this is likely to be very challenging. SCORM is completely centred around the course being in a browser and the course launch having been initiated by the LMS.

One of the main reasons for xAPI's existence was to create something that didn't have this limitation.

Adapt does not yet have xAPI support - but we are working on it. If you want to get involved, please do feel free to join the conversation over at https://gitter.im/adaptlearning/xAPI