No they don't. My roommate moved out a few months ago, I watched him fill out the mail forwarding form (with his name and my/our address). Not only did no confirmation letter show up in my mailbox -- in fact I stopped getting my own mail for several days and when I confronted the USPS worker, he said, "Oh, I thought your apartment was vacant now." I got pretty mad and he just shrugged, not even an apology.

I had to get my car's title reissued from the DMV (I had just bought it off my roommate as he was leaving), and also had a paycheck disappear (was working 1099 remotely and paid monthly via check) because both things were coming in the mail that week and disappeared never to be seen again. (Luckily the guy I was subcontracting from paid for his own stop payment and reissued the check)