Is there a way to have the update link added to the submission?

Is there a way to have the JotForm update link added to the submission in the Google Sheet?EX) Columns across the top: "Name", "Email", "Phone #", etc..., "Update Link"

Do you mean the "edit link"? If so, the edit link is already included when you integrate your form to google spreadsheet. Please check your spreadsheet and look for the "Edit Link" section.

Let us know if you are referring to something else.