Currently, the app will resume a course that was started online in the app as long as the device is Online (has internet connectivity), however, if a Learner is to start a course online, and the wish to complete the course offline, as soon as the hit the download button, any progress made will not be saved.
This happens with packaged courses (SCORM 1.2, 2004, and xAPI) but not with regular Learning Objects such as assessments or objects.