To be clear: there is an Offline mode and Online mode.
The Offline mode is just a contact form. When submitted, it gets emailed to the site admin (or whatever email address is set up). As it stands now, if you’re looking at collecting email addresses, its probably not the best tool to use. Offline mode saves nothing to the database.
The Online mode is where the chat takes place. All visitors, chats, and their information are stored to the database and accessible later on. Conversations are viewed one by one, there isn’t really a spreadsheet view of all email addresses that have been submitted.
That being said, I think there’s some merit to storing the info and I’ll gladly put it on the list of features to add.
Hope this clears things up!