So I got it working and uploading the emails to Google apps mail. A bit confusing as Google mail has "Sent Mails" and "Sent Messages" but it works. I can now receive and send emails from Mail.app through Google apps mail.
The last struggle I have is that the sent messages won't show up in the normal "Sent" part of Mail.app. I have been playing around with the settings in Mail.app but I don't get it to work. iCloud/MobileMe IMAP is working fine with the Sent mail.
Any suggestions or does anybody have the same problem?