No, especially considering that QR doesn't actually ticket short-haul flights in C.. they are ticketed in F (even though the in-flight experience is clearly that of a C class flight) - however i'm not quite sure how this works with redemptions.. If it's an F-redemption, it might not quite be worth it.
In any way, this does mean in theory, that you'd have access to the Al-Safwa lounge.. once it opens. Until then, Al-Mourjan it is.