If you can source the data using one of the connection types Tableau Supports All Technical Specifications | Tableau Software then you can analyze it.
You haven't specified how you're going to get this email data so it's a bit hard to say. What I can tell you is that out of the box Tableau doesn't connect to an Exchange Server or IMAP server. You might be able to find an ODBC driver to do this, or you could write your own custom Web Data Connector script to connect to your mail server and parse the information into a format suitable for Tableau.
The easiest thing would be an extract of some sort i.e. Excel or an export into a database.