The only time an internet connection is needed is when you activate your software. If you do not have an internet connection available on the computer where Version 6 is installed, then you can use the form at http://licensing.mackichan.com/Activate from another computer. Use the computer ID from the computer where Version 6 is installed.
If you have the What's New side panel open, Version 6 will attempt an internet connection to refresh its content. You can disable this by closing the What's New side panel using the Close item from the Actions menu.