Unlike Microsoft Office apps such as Word, Outlook is not integrated as a COM addin (it's done using an Exchange Client Extension), and doesn't expose a shared interface so I'm fairly sure the session generated automatically by FileSite isn't available to you.
Obviously you'll have an implicit connection if you're developing and registering a custom iManage command, however I'm guessing your requirement sits at a much higher level.
In that case you'll need to manage a separate (new) connection, which is only complicated in cases where your users may legitimately need to manage multiple servers, or where you may have Offsite installed and have to cater for that also.
For a substantial number of iManage implementations that's not a requirement however, so it's just a case of determining the "default" or last-used server (from the registry) and performing a trusted login