No
New users are not the problem; it's the quality of posts that needs addressing - from both"veterans" and "newbies".
While it does seem more frequent that new users are creating bad first posts, I see just as much guff from users who have accumulated a few upvotes over time.
My suggestion would be to have a constant ban threat.
Any time any user wishes to make a new post (question or answer), their latest n
posts (3 for example) must have a non-negative sum. In the event that, this sum is negative, these posts must be edited to an acceptable quality before they are allowed to post again.
The aim would be to make users think of their recent contributions, while existing bans aim to stop repeat offenders.
This does still weigh more heavily on newer users since if they have less than n
posts, then they are judged based on all of their existing posts.
I don't think we will ever find a way to stop all bad questions, but stopping those users that stay from repeat offending, (I hope) will make it a much more pleasant place for everyone.