PP: No. There is always a risk of appearing over-eager; if you've told them twice that's sufficient. However, if your child is wait listed, you should reiterate it.
First choice letters can help if they're sincere, because it's to a school's advantage to fill fewer slots. If a school has 25 slots for ninth grade and is nearly certain they'll yield 10 admits, that means their calculations for yield are based on 15 slots, not 25, which should decrease the margin of error by 40% (theoretically, anyway).
Schools that compete for applicants do not talk about their applicants during the process. There was a thread on this a few weeks ago — among other concerns it could be an antitrust violation and they're all too busy to be gossiping at this time of year.
Telling multiple schools they're your first choice: In a practical sense, you might decide later to change schools and you can be pretty well assured that the schools where you reneged on your promise will not view it favorably. In addition, if your child is at an independent school now, the person who coordinates placement will probably know you don't have three #1 choices, and that could expose a loose allegiance to the truth when he or she advocates for your child.
Regardless of the "enforcement," I'd think people would be decent enough not to be intentionally dishonest. That kind of thing has a habit of catching up with you and it does not serve children well. It's a long four, seven, thirteen years. Truism: Parents who behave poorly (see: Dishonesty, intentional) are more likely to have children who behave poorly. Corollary: Parents who behave poorly are more likely to blame their children's poor behavior on the school.
Peter
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Disclaimer: The anonymity here makes me uncomfortable; it's easy to be uninformed, personal, or simply mean-spirited if people don't identify themselves. For that reason, I have an account so you know whose words you're reading. I have more than 20 years' experience as a teacher and administrator in independent schools, and I have counseled hundreds of students in finding their next schools. I hope I can be helpful to some folks. If you don't like something I've said, you're in good company — there's a long line of past students and parents ahead of you.

If you want to chat further, please feel free to contact me offline: peter <at> arcpd <dot> com