ok: I can ensure you that in a random completed puzzle, like the following, if you choose two of the letters,any combination, there is only one way to conect them. This is not only limmited to those letters, but to any road tiles you want to choose. As this is not limited just to this specific puzzle, i think we can say "In a completed puzzle, all the roads are conected to each other by only one path". This is the same as saying "in a completed puzzle, there cant be a flower group completelly surrounded by roads, taking expansion soil as non road" or saying "In a completed garden there cant be a closed perimether made of roads, be it square, rectangular or irregular" or any other way of saying that your head can think of
Graphical example: http://imgur.com/mm31za1