Do researchers at schools that publish good journals get priority in publishing in those journals? Take mathematics, for an example.

Do Princeton math professors get any sort of priority / preferential treatment in publishing in the Annals?

Do Duke math professors get any priority in publishing in the Duke Mathematics Journal?

What about more applied places - do NYU Courant professors get any priority in publishing in Communications in Pure and Applied Mathematics?

My question is generally about priority / preferential treatment, not about specific schools or journals.
The answer is certainly not - not officially anyhow - except insofar as being a well known mathematician (which someone who is at a place like Princeton typically is) makes it easier to get one's paper accepted to a fancy journal. That effect is likely real (though of a magnitude that would be difficult or impossible to measure, and hopefully not too large), but it typically applies on a more global level rather than a journal-locale-based level.