Someone has to pay the bill, which means someone will go to jail. The only reason online DDoS attacks are perpetrated successfully is because of the relative ease of execution and the anonymity provided by an internet connection. Still, even with the loosely connected identifying information available about your internet connection, the FBI is issuing warrants [1] for participants in recent DDoS attacks. A paper campaign's only chance for success would be if individuals physically printed and mailed the letters anonymously by posting them in a public mailbox. Investigators would have to rely on traditional investigatory methods like finger prints and mysterious printer identification dots [2], which work much slower.
1 - http://www.google.com/search?q=fbi+ddos+anonymous+warrant
2 - http://boingboing.net/2008/10/23/howto-read-the-secre.html