W3 Total Cache with 'Members' plugin?

I’ve got a fulltime https site with private membership using the ‘members’ plugin (http://wordpress.org/extend/plugins/members/). Only students with accounts can login and view the tutorials and add comments. Will I gain anything by adding W3 Total Cache and can it remain secure? In my initial testing I realized that after W3TC was enabled I no longer needed to login to view content, is something set incorrectly or is caching a bad idea for this type of site?

http://wordpress.org/extend/plugins/w3-total-cache/