Just as the title says, when you delete your Facebook account, will the messages you sent still appear in the inbox of those you sent them to?
Your name will just appear as "Facebook User" (written in grey) in the inbox of the recipient. The message will still show, but not from whom. It works exactly the same when someone is blocked. This does not happen instantly, it takes a few days for it to appear as "Facebook User" on the other end.
I've seen this on my facebook profile.