Rather, don't put LIVE cats in mailboxes. At least we know the boxes get checked daily, but man, why do people gotta be jerks? The kitten in this archive photo was rescued by the postman, but just think of the trauma to the poor kitty and the damage done to mail in the box.
You can, however, put all kinds of cat inspired stuff in the mail. Why not use the fun printable template for a cat-shaped envelope while you're at it? The Paper Pastries company (-Hi, Margaret!-) has you set up for cat-themed stuff in their shop and inspiration on their blog. Check the #catmail and #sendmorecatmail for tons of awww and ideas.