Not unlike publishing free/busy time from your Outlook calendar, this article discusses publishing email activity in an attempt to better inform those making requests of you via email. (Source)
…it periodically checks the user’s email load based on specific measurement parameters chosen by the user – unread messages in your inbox, total number of messages in your inbox, or how much mail you’ve recently sent. After an initial 12-hour analysis, courteous.ly determines the user’s email habits and what constitutes “light,” “normal” or “high” e-mail amount. It then updates the user’s status of email volume level every 10 minutes, which is reflected in an individualized courteous.ly link.
May have to play with courteous.ly and gmail.