I always send mine like this:
Contact's name
ATT: Any Soldier
Address
Address
That way they know the mail is not specificaly for them, but is for someone random in their group. It will be delivered as long as it has a specific person's contact name BEFORE the ATT: Any Soldier line. Adding the ATT: Any Soldier lets the contact know that the box is not for them specifically from someone they know back home but for them to give to someone who maybe doesn't get as much mail as someone else.
Not sure if that made sense.
Essentially: Do add the ATT: Any Soldier, just make sure you have a contact name before it. If you don't have a contact name and send addressed just to "Any Soldier, it can't be delivered. You used to be able to mail a box addressed solely to "Any Soldier" and it would be given to a random soldier.