Hopefully not since 2003 when the FTC had a court enjoin that specific company from making misleading statements about renewals in their postal mail.
The mails they send out now look like this:
"As a courtesy to domain name holders, we are sending you this notification of the domain name registration that is due to expire in the next few months. When you switch to Domain Registry of America, you can take advantage of our best savings. Your registration for _______ will expire on _____.
You must renew your domain to retain exclusive rights to it on the web, and now is the time to transfer and renew your domain from your current registrar to the Domain Registry of America.
...
This notice is not a bill. (bold) It is rather an easy means of payment should you decide to switch your domain name registration to Domain Registry of America."
Followed by the pricing table and write-in order form. Still junk mail, but not falsely representing themselves as your current registrar.
I get these mails all the time too, and unfortunately I actually have to pay one of them. Some 12 years ago or so, I helped a neighbor who runs a local charity by creating a website for her annual event, pro bono. Even though she paid for the domain, the billing contact info was changed to my address (perhaps by her, when someone asked for a technical contact), and transferred to DROA. I don't live in that area anymore or have contact with this neighbor, and I'd rather not track her down with a bill nor let the domain of her charity expire, so I've been dutifully paying the marked-up DROA renewal every year.