That’s a big question, with no simple answer. One thing we know for sure: the “New Testament” did not exist in its complete form until the end of the first century, and the earliest of the books are generally conceded not to have been written until 15-20 years after the death of Jesus. So the Church survived for the better part of a century without possessing what we call “The New Testament”. The oral tradition, passed down from Jesus and the disciples to the next two or three generations, would have been crucial in the formation of the character and doctrines of the early Church.
In the Eastern and Roman Catholic communions, Tradition is a very important component of the faith, equal or nearly equal in importance to Scripture. It is taken for granted that God revealed himself not only in Scripture, but in his continuing inspiration of his Church, through the writings of the Holy Fathers, the Creeds and Councils, etc. In contrast, Protestants nominally acknowledge the Bible alone as a reliable source of Christian doctrine. Even there, however, the great founders of Protestantism had immense respect for theological tradition and studied it in high volumes. If you compare medieval Catholic theology, the writings of Calvin, and the sort of theology produced by, say, Nazarenes, you will find that though the Nazarenes are nominally on the Bible-only side with Calvin, Calvin researches, argues, and thinks more in the style of a Catholic scholar. The best of the Reformers saw themselves as part of the historical church with its orthodox theology, not as freelance Bible interpreters emoting their way through the Bible in the “me and my conscience and my Bible” sort of way that is unfortunately so large a part of the American religious landscape.
Yes, they could, and to some extent still do, in the Roman and Eastern Churches. Less so in most Protestant churches, especially in their American branches. And even less so in the kind of churches that BioLogos leaders tend to frequent, where the focus (there are a few exceptions) is much more on Bible and much less on theological tradition.
I’m glad we can wrap this up on a note of agreement, though of course John Harshman might well choose to argue about who exactly are “the founders of Christianity.” From the point of view of historical orthodoxy, not only Jesus and Paul but the theologians who formulated the Creeds and early council decisions would also count as “founders of Christianity”; the doctrine of Trinity, for example, is central to Christianity in both East and West, and the fully formulated doctrine of Trinity is not directly from Jesus or Paul or the first disciples, but is the product of a few centuries of sophisticated debate and discussion within the Church. Once it was settled, the teaching about Jesus (as understood in Trinitarian doctrine) because just as important a part of core Christianity as the teaching of Jesus, as recorded in the Gospels. I strongly suspect that at least one person here (I’m not referring to you, or even to Harshman) would like to completely get rid of “the teaching about Jesus” and limit Christianity to “the teaching of Jesus”, but whatever the religious or spiritual merits of that proposal might be, such a move would not be in line with orthodox Christian teaching, and would amount to a radical reshaping of the Christian religion as it has been historically known.