STUN servers are only required for NAT punching, they don’t relay traffic. Only TURN servers are used as relays in the event that a direction connection can’t be established.
I had a mistake in my post where I confused TURN and STUN. It's been a while since I actually tried to do this stuff. The stackoverflow post has details on how I tried to achieve connectivity, if you check that you will see that yes I used STUN.