I have tested Mail.dll with WinForms using C# as I needed to send an email via IMAP and your example allows me to send via SMTP then upload the email to IMAP 'sent items'.
Is the same functionality available using MVC4?
Yes it is.
You can use Mail.dll in ASP.NET MVC project without any problems.
Please remember that your web application must have enough permissions to open connection to the SMTP or IMAP server.