Yes and no. When items are shared during class via the "Present" menu, they will be presented again when watching a recording of the session via the Playback Room. However, as Engageli is not designed to be a cloud storage service, there is not a way for Learners to access these items directly from outside Engageli.
This same limitation also applies to any items that are uploaded to the classroom's Content Manager. The Content Manager is designed to allow Instructors to upload content to the class ahead of time for easy access and organization; these items are not designed to be available directly to learners as they might be if they were uploaded to, say, Dropbox or Google Drive.