Question: Does having more than the required number of teacher recommendations help in any way?
Most colleges prefer that you stick to the suggested number of teacher recommendations. An extra one won't take you out of contention, but before you solicit references from every instructor who ever gave you an "A" or smiled at you in the cafeteria, do keep in mind that there's an old saying in the admission world, "The thicker the folder, the thicker the kid."
When is it appropriate to send in an unsolicited teacher rec? Typically it's when one teacher knows you inside out but doesn't teach you a major subject or hasn't had you in class since 9th or 10th grade. For instance, if you're the school yearbook editor, then the yearbook advisor probably can speak to your intelligence and sense of responsibility (and probably your sense of humor, too) more than any other teacher you've encountered. But if he or she taught freshman photography or sophomore earth science, you probably want to pick someone else to do your primary reference(s).
Overall, you're far more likely to annoy admission officials with an abundance of non-required recs than you are to impress them with a pile of extras, however glowing.
Hope that helps. Good luck with your applications.