I think so. Although I must emphasize that it is not easy and we should not take the task lightly. What I mean is that we cannot allow ourselves the luxury of becoming lazy, accepting what the texts tell us as a record of what actually happened. We must develop a hermeneutic of suspicion as second nature. Reading against the grain must be embraced as our best friend.
If we have one, we must be conscious of our own faith perspective, be willing to set it aside so that our historical task does not become a servant to own theological beliefs.
Likewise, we must acknowledge the ways in which the canon has dominated the field, and all the assumptions that this has brought with it - including the assumption that the canonical texts are reliable and accurate representations of Jesus and early Christianity.
We must also revive the old historical methods but within a contemporary academic context, revising them with theory from the cognitive and social sciences as well as from philosophy and literature. Even though they must be improved, I truly feel that nothing can replace the old methods, and we should be teaching them to our students, undergraduates and graduates alike.
I think it is important for us to distinguish what kinds of history we are after and what kinds of history are possible to recover from the early Christian documents. I am very comfortable, for instance, reconstructing the traditions of the people who created and recorded the document. These theological texts reveal quite a bit of information about what the early Christians were thinking and practicing whether it be from the Gospel of Philip, the Gospel of Mark, the Gospel of Thomas, the Gospel of Truth, and so on. The diversity of thought and practice is staggering. And I imagine that I will spend my entire career trying to sort this all out.
The documents I am most thankful that have survived are the letters of Paul. Without them I don't think we would have a chance to reconstruct early Christian history. We would be completely lost trying to recover anything of value in Acts. But the letters of Paul are autobiographical, and with them we can begin to see glimpses of Jesus' family running a church in Jerusalem, and so forth.
The type of history I am least sure about recovering from these theological texts is actual events in the life of Jesus and actual words that he said. I am scared of the historical Jesus. It is so easy to invent Jesus in our own image, and to create a methodology to support that endeavor. On top of that, the texts are intentionally portraying him as they do by authors who believe him to be God. So whenever I think about trying to write about the historical Jesus, I tremble and put down my pen. It is still beyond me how I go about this as a historian.