No, the message is not logged in the DB, at least not in the chat box portion. I can verify this because I store the PM ID numbers that come back with each message for the CB stats. When the stats service goes down and I miss it on reboot, I can see a "space" in the ID numbers. When this error is hit on my end, there is no gap.
I no longer have pmdev access here (as per my own request years ago), but I seem to recall that there is a field in the user that stores the last message that that user posted, and is used for comparison to get the whoa-cowboy rejection message. It appears to me that the message gets to the server far enough to be saved to the user record, but fails between that and actually putting it into the CB table. I'd argue that it shouldn't get saved to the user record until it has been successfully saved to the CB table (or both as part of the same transaction), but that's just arguing about error handling and doesn't solve the underlying error.
(Thanks, choroba, for posting this.)