Actually your function works as you described.
I copied your function into a page template on my site without modifying it at all. I tested it with my main user, which has posted, and it said I had posted.
Then I created a dummy user that has not posted. I tested the same page and it said I had not posted. I also posted a post backdated more than 30 days, and it still said I had not posted within the last 30 days.
All of that is by design.
A couple of points to keep in mind:
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You aren’t specifying in your query which type of post is being retrieved. Are you sure that the user you are testing with hasn’t posted any type of post? i.e. a custom post type, a page, a contact form via a plugin, etc.
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Your code is also always checking the currently logged in user. Make sure that’s what you want.