I am sure this can be done several ways, the question is how do you want the transition to look like? Is it a morph or does the line animate to form the letters one by one? Is the file you posted the final look? Let us know and we can provide better feedback.
I think you can either use animated masks to ceate the illusion or use a path that you animate to form the text and apply a stroke to that. With the path it's easier if you animate in reverse- start with the final position, draw the line with the text formed and then work backwards to unravel and flatten the line. The trick is to design a look that will allow you to have the text formed by one continuous line.