The character could possibly become drunk immediately after sending the "I am not drunk" message, so you'd need to check if the character was still not drunk after sending the FriendNet messages. But assuming that drunkenness lasts much longer than it takes to send the FriendNet messages, you could be sure that if the character was not drunk before and after, then the messages in between were also valid.
Yes this would work, even though the message could get garbled including the checksum, you make the first set of characters be a checksum for the rest. If the checksum or message became compromised it would fail validation. This is the best solution so far. Send it with every message.
Or even better, depending on length limits on message, you could prepend every message with a sentence to check. If it is not OK, discard the entire message. If it is, process the rest.