Ime, it’s a teacher issue, not an adcom concern. The teachers want a private way to communicate, one educator to the colleges, without some hs kids or parents getting involved beyond some initial input. I have never seen an adcom react in a way that doubts the letter because the Ferpa went unsigned. Or even mention it.
Each applicant has to make his/her own best decisions. Do what makes you feel comfortable. Remember, during a review, they don’t have time to second guess what’s going on. Their impression of you is formed by much more than this one point.
If you do send a note, keep it short and to the point.