By design, the "member" access level is for employees who use the system to sign up for shifts, submit availability, submit/receive trade requests, and request time off.
If you'd like to add messaging in addition to this, create a new access level and use batch edit in the member database to change everyone to this new access level. The only setting you will need to enable is "View data for all members." This will enable the list view of the member database (remember, prior to this, members only saw "My Info.").
Will these employees be able to see all fields I track in the member database? Good question!
Each field in the database has a checkbox to make it a "hidden field." When a field is hidden, access levels that do not have access to view hidden fields won't even know the fields are there!