Yes, even if the user was anonymous.
There is not REST API that takes a chat log, but their is a training API
http://www.botlibre.com/rest/api/train-instance
It takes a POST XML entity like,
<training operation="AddResponse">
<question>Hello there</question>
<response>Hi, how are you</response>
</training>
You could probably also POST to chat-log-upload URL that the "Training & Chat Logs" page uses with a HttpPost request that was connected.
Yes, I am a developer of Bot Libre.