This may seem like a good idea. It doesn't require direct Internet access to the internal network. The e-mail is accessible from anywhere. But this solution is not very attractive from a security viewpoint. Corporate e-mail is unprotected after it leaves the corporate gateway.
Providers exist with solutions that are free or inexpensive.
These include ZixMail , Ensuredmail , HushMail and Disappearing, Inc. . There are some potential hidden dangers. The implementation must ensure that the connection is terminated after a short time. Further, we must keep in mind that we are allowing access from the Internet all the way into critical systems. Each has benefits, each has vulnerabilities, so each must be secured.