you can definitely followup if you don’t receive feedback after one month.
This won’t lead to negative outcomes, while it could be beneficial in some cases.
As an example, after applying to Oliver Wyman I didn’t receive any feedback.
After one month I called the recruiter and asked which was the status of my application.
She looked at my CV, liked it (it seemed she had never seen it before) and invited me on the spot to an interview.
In the end I received an offer from Oliver Wyman. I am not sure they would have ever invited me if I hadn't called that day.