I could be opening the proverbial can of worms with this one.
First, let me say that I believe there were real historical people behind many of the stories and traditions of the Hebrew Bible/Old Testament. I believe there was a real Daniel, Ezekiel, Isaiah, Moses and so on. However, I can't indisputably prove any of them really existed. I can point to details in the biblical accounts that suggest their historicity. For some figures, there are references from archaeology that suggest their existence, but those are always bitterly disputed (For example, the Tel Dan inscription's mention of the "House of David"). For figures whose historical existence I was unsure of, I used to consider the NT references to them as validations of their historical existence.
For example, I thought that Jonah must have really lived, even though his short book reads a lot like a fable teaching a moral truth, because Jesus mentioned him, referring to the sign of Jonah in Matt. 12:39-41 and 16:4 (cp. Luke 11:29-32). Jesus also mentions Abraham, Isaac, Jacob, Moses, and Elijah fairly frequently. I believe, though again I can't prove it, that these figures have a historical origin. Jonah, on the other hand, quite possibly has only a literary origin. Is the truth conveyed by his book and used by Jesus in the NT predicated on his historicity? After giving the question a lot of thought, I don't believe that it is. The story teaches the same moral whether it really happened or not. The story exists as an example for Jesus to use to draw a parallel to his own situation. The comparison of Jesus being in the tomb 3 days just as Jonah was in the whale for 3 days does not depend on Jonah having existed and endured the events of his story. The comparison is valid because the story existed that provided the literary parallel.
[This extends to Jesus's full use of OT figures in Matt. 12:39-42 and Lk. 11:29-32. He's using an argument structure the rabbis called qal-va-homer ("light to heavy") to reinforce the judgment of wickedness and evil against the current generation of Jews. This type of argument is a comparison ("how much the more so" or a fortiori), so he's drawing parallels between the situation in Jonah and the situation with Solomon. His argument is that the men of Nineveh believed Jonah and the queen of Sheba believed Solomon; he is greater than both; therefore Israel should believe him and will be held accountable at the last judgment for it. The claim that the men of Nineveh or the queen of Sheba will rise up at the last judgment is part of his rhetoric. The argument is theological, not historical, in my opinion. (Paragraph added -- 5/15/08).]
It would be a little bit like today's culture where we can reference fictional characters that have reached iconic cultural status. When we mention their names, we evoke their story, known to most people at least in broad outline form. This is especially true of Shakespearean characters such as Romeo and Juliet or Hamlet, or LOTR characters like Frodo and Gandalf whose public profiles were raised by the recent blockbuster movie trilogy, or a literary/film phenomenon such as Harry Potter. When we reference these fictional characters, we are tapping into the power of literature and art, not history. No one assumes that Frodo was a real person just because they heard a friend mention him by name.
Of course, no one in today's culture is believed to have special knowledge or authority to speak about past people and events in the same way that many Christians believe Jesus or the NT writers in general had a unique perspective on history informed by the divine inspiration of their words. If these characters weren't historical, what does that do to inerrancy for either the OT story or the NT reference to it? The answer, in my opinion, is that it does nothing at all to inerrancy or inspiration. Neither reference is explicitly claiming to be telling a history. James isn't wrong to refer to Job (James 5:11) and claim his patience as a virtue that believers should attempt to emulate. He can refer to the main character of a well-known story without necessarily claiming that Job was a real person. The book of Job itself never claims to be history. It's set in the land of Uz - unknown as an actual place in the ancient world - and begins with the Hebrew equivalent of "Once upon a time..." Even the ancient rabbis believed that Job was a parable, not necessarily a real person. Claiming that Job or Jonah must be real historical figures would be like trying to find the historical personages behind Jesus's parable of the Good Samaritan.
The question is more difficult the further back one goes to the "legendary" material in Genesis. Did humanity really start with just one man named Adam (which literally just means "man")? Was Noah a real person? Did the flood really happen? Again, I think the answer is yes, but it is a belief based on a faith commitment, "the conviction of things not seen" (Hebrews 11:1), not on anything I can prove with evidence.
Adam is hardly mentioned at all in the NT. Jesus never mentions him by name, and I could find no direct allusions to Adam, Eve, and the Garden of Eden in the Gospels. Luke's genealogy of Jesus goes back to Adam (and includes Noah), but so many genealogies seem to be handcrafted to make a theological point that I don't think we should use them as historical evidence (cp. Matthew's genealogy that obviously skips generations and conveniently divides history into three eras of fourteen generations each).
Noah appears a few times in the Gospels, usually in a comparison of the wickedness of his days with that of the coming end times (see Matt. 24:37-38 or Lk. 17:26-27). He also appears in the famous chapter on OT faith in Hebrews 11. He's also part of the retelling of the biblical account of God's interaction with mankind and mankind's failure that appears in 2 Peter 2. For all of these references to Noah, the biblical story is what's important to give meaning to the NT reference, regardless of whether Noah was historical or not .
Most of the references to Adam in the NT come from Paul who specifically contrasted Adam and Christ theologically (see Rom. 5:14; 1 Cor. 15:22, 45). This is demonstrated most concisely in 1 Cor. 15:22.
1 Cor. 15:22 (ESV)
For as in Adam all die, so also in Christ shall all be made alive.
Paul has mapped out a theological system where he uses OT figures and events as types which find their ultimate fulfillment in Jesus and the Church. Paul's theological use of OT figures falls under the same issue. His theological point is based on the story as recounted in the Bible. The meaning and theological significance of the Bible transcends history. It is rooted in divine revelation, not in our ability to prove that all of the characters were real historical people.
Therefore, it seems ok to me to admit that some of the characters may be fictional. I believe many are historical, but the fact that a NT writer refers to an OT character should not be used as evidence that the person really lived. The biblical writer had a purpose in using that reference. That purpose usually did not include corroborating our assumptions about the historicity of the Bible.
To conclude, let me stress that I am NOT saying all OT figures are fictional characters. I have circumstantial evidence that strongly suggests there was a historical person behind many of them. My point is that the NT was not concerned with that question. The NT writers referred back to the entire body of biblical tradition that was known in their day. They did not attempt to divide the material into historical/non-historical. The question probably didn't even occur to them. They used the material because the story helped them make a theological point or draw a parallel that their audience would have understood.
I'm still working out my ideas on this question, so my thinking might be a little fuzzy. My intention was addressing the issue with claiming that Jonah or Noah or whoever was a real historical person solely based on the "proof" that the NT mentions him. I hope that I've at least stimulated some thought on that question.