I now have a product for you to test out.
As of now, thread visibility is not affected, only posts as you originally requested, but before I upload the product in the "vBulletin 4.x Add-ons" forum, I want to give the option for the thread to be auto-approved as well, and this will take some time for me to figure out.
So, download the attached XML file, then follow:
AdminCP -> Plugins & Products -> Manage Products -> [Add/Import Product]
And then browse to the downloaded XML file and click "Import."
Then go to:
Settings -> Options ->MarkFL: Auto-Approve Posts On Reply v1.0
And enable the product, and set the other options as you choose.
Please let me know if anything does not work as you expect or any other feedback for improvement. In the meantime I will be working to give the option for auto-approving threads.