Yes, and for most private mail that's perfectly fine as long as there is adequate postage. People who are required to furnish an accurate return address include senders of prepaid mail (you know, where it's printed on the envelope with a number), distributers of periodicals, senders of priority and registered mail, and a few other similar examples.
In that case there'd be no tracking of who is mailing whom, but instead just how many letters someone is receiving.