Yup. Remember, the only thing we're told in the Gospels about Jesus *writing* is whatever he wrote on the sand in the episode with the Woman taken in adultery.
A shocker for me was figuring out that all the people who do the "Paul perverted the faith of Jesus" business rests on an obtuseness -- you see, the Current Scholarly dating says that the Pauline epistles (the authentic ones, at least -- Hebrews is pretty late) PREDATE the Gospels. If you want to believe that there was a written gospel message for Paul to react against you have to believe the Traditional dating in which Matthew writes in the 40s. Odd.
Of course, there is also this connection--the large amount of common material in Matthew/Mark/Luke, which is often said to have come from a common verbal collection of "Jesus sayings" preserved by those who'd seen Jesus alive.
That was part of this "teaching of the living church".
What I find interesting is that these parts of the teaching of the living church could remain verbal as long as those who saw the events remained alive, but would almost naturally become the written Gospels as that generation died.
The letters of Paul (and Peter, James, John, and company) appear much more plausible against the background of the living tradition than against a background of written Gospel.