Can I setup connections that don't have an email address?

Yes

Since we don’t validate email addresses you can setup a “fake” email address for employees who don’t have email, but we ask that you don't do this so we don't get bounced emails. At a minimum, set up an alias with a forwarding email on your server OR you can also alternatively setup these employees as virtual connections. (See the video tutorial or knowledgebase article on connection setup.)