I forgot I posted this...got busy again. Yes, I believe GT Sport Closed Beta does support the Logitech G29. Unfortunately, I still haven't upgraded my Logitech wheels...so I am still playing with the thumb sticks and don't want to comment too much on the gameplay until I can use one of my older wheels (or finally cave and upgrade).
I will say this...the online racing still has issues, but it is fun. I'm just bummed they took out the offline single player arcade mode after one of the earlier updates.
If you haven't gotten Driveclub, you should consider picking it up. It got patched to include a hardcore mode that makes the arcade racer feel more like a sim...hard to play on the sticks in pro mode, but arcade is way too arcade for me. It is a beautiful game and its weather effects are unrivaled.