Is there anyway to search on a non-primary email address?
In Search Builder (Top menu > Search > Search Builder), you can specify which type of email address you would like to search for (on the demo: Home, Work, Main, etc.). By linking the searches with "Also include contacts where", you can specify each type to include (see image).  It doesn't cover the specific search "emails that are not marked primary," but it will search emails that are not primary along with the primary ones as well.