As of latest 3.4.x update, "post-download the game is entirely DRM-free." statement is not right. After game start the game itself validates DLC ownership. Confirming it for Paradox Launcher v1/v2 and GOG's stand-alone installer: if you're not logged into your PDX account in-game - you can't use DLCs at all. Even if launcher v2 shows DLCs as active (and owned).
Topic on Talk:Stellaris
I've updated the note.