Doubt it. they would need to spend more time on each car to inspect them to improve on most of the complaints... and time is something they dont have, especially now that they lost so much time due to closures.
I drive by a tesla repair shop (not a 3rd party, but Tesla owned one), on my way to work every day, and last week I saw 2 model Y's in there. Now this shop doesnt do test drives, they dont do deliveries or paint at that shop. So I wonder what they are in there for. Hopefully nothing serious. But seeing how few have been delivered so far, and already seeing 2 in the shop makes me worry about mine. I ordered black though, and from the looks of it thats at least 2 to 6 months away... so hopefully by then any kinks found with first releases are ironed out.