Did the importance of the resurrection increase as the New Testament was written?

No, given that works don't show a clear trend and were written by different people for different purposes.

This also 'begs the question' given that it seems to assume that the Resurrection could somehow be 'unsupernatural'?

No.

The importance of the resurrection is highlighted starting in Genesis. Jesus death was the fulfillment of "Satan bruising his heel" from Genesis 3:15. Without the resurrection, that would have counted for a lot more than a heel bruise, but with it the promise is proven true and Satan's head is crushed. Likewise, Isaac being given back alive points to a sacrifice that gives life. Many more examples could be given from just the oldest handful of Old Testament books.

The story continues to develop all through the Old Testament. By the time we come to the New Testament accounts in the four Gospels (which date as the earliest content in the NT even through penned after a few of the letters) the authors are able to talk about the resurrection as both a certain fact and the culmination of a long foretold story. Jesus himself speaks of his own resurrection as the key piece in the events that will unfold on his own life.

While no case can reasonably be made to defend the thesis on your question, it should come as no surprise that the actual language used to describe the event becomes more plain in the letters addressed to churches that did not witness the event. As neigh-sayers arose in the community, the reminders to true believers that address the importance of the core understandings of Christianity are given head on. 1 Corinthians 15 stands out in this catagory, however beyond a few letters which emphatically state the importance of the resurrection to the faith, any attempt to impose an artificial timeline on this as a developing idea will fail in light of some of the latest written texts hardly mentioning the fact and some earlier ones giving it lots of attention.

Rather, the original context of each book and writer should be examined to understand it's take on the subject. Paul had a specific reason to emphisis this doctrine is such clear speach to the Corinthians; and it wasn't that he had a new agenda to push.

Allow me the liberty to rephrase your question:

Did the concept of Resurrection develop over time?

Yes.

The ancient Hebrews did not seem to have any conception of life after death. In Job and the Psalms, we start seeing hints that Israelites envisioned some existence after death, but not as anything very exciting. If you've read any Homer or the Gilgamesh epic, you'll remember that the dead go to a shadowy, dry place. But it's important to understand that, unlike the Greek concept of Hades, Sheol wasn't a place where souls existed, but where whatever was left of the dead's body and spirit was housed. It's not clear that the writers of the earlier books in the Old Testament envisioned anything more than a grave when they used the word.

By the Second Temple period, Jews began to develop more sophisticated cosmologies. We start getting hints of bodily Resurrection:

Daniel 12:2 (ESV)
² And many of those who sleep in the dust of the earth shall awake, some to everlasting life, and some to shame and everlasting contempt.

But even then, it's not clear if the Biblical prophets (outside of Daniel) were envisioning people actually rising from the dead. Ezekiel 37 (the dry bones passage), for instance, was probably a statement of hope for the restoration of the nation of Israel.

Jewish writings in the time between the Old and New Testaments show even more development of the idea of Resurrection, which always had strong nationalistic and (during times of occupation) revolutionary overtones. But the idea was that at some point in the future, God would gather up all of His people and restore them to life all at once. Nobody would have pictured one man rising from his grave as the (or even a) Resurrection. Certainly the Messiah would not participate in the Resurrection, except to make way for it to happen, since he wouldn't die.

When we get to the time of Jesus, we suddenly see the Christian conception of Resurrection appear on the scene. It draws strongly from the inter-testament ideas, but in a fairly radically altered format because the Messiah Himself dies, is buried, and resurrected. Sometime later, the general Resurrection as envisioned by late, Second Temple Jews was predicted—along with the return of the Messiah to complete His work on earth.

How did the concept of Resurrection develop in the New Testament?

Surprisingly little.

Our earliest church documents are Paul's letters to various primitive churches. While it does seem that Paul warms to the subject over the course of his ministry, he does not alter his theology. In Galatians 2, Paul lets us know that his theology was shared with the leaders of the Jerusalem church (James the bother of Jesus, Peter, and John). His dispute with them was not whether the Resurrection of Jesus occurred or what it meant, but whether or not it replaced the Mosaic Covenant.

In First Corinthians (ca. 53-54 AD), Paul gives us one of the earliest formulations of the Christian view of Resurrection:

1 Corinthians 15:3-8 (ESV)
³ For I delivered to you as of first importance what I also received: that Christ died for our sins in accordance with the Scriptures, ⁴ that he was buried, that he was raised on the third day in accordance with the Scriptures, ⁵ and that he appeared to Cephas, then to the twelve. ⁶ Then he appeared to more than five hundred brothers at one time, most of whom are still alive, though some have fallen asleep. ⁷ Then he appeared to James, then to all the apostles. ⁸ Last of all, as to one untimely born, he appeared also to me.

Many scholars think this represents an even earlier tradition that might have been a creedal statement. Paul goes on to affirm that there will be a general Resurrection in the future:

1 Corinthians 15:21-22 (ESV)
²¹ For as by a man came death, by a man has come also the resurrection of the dead. ²² For as in Adam all die, so also in Christ shall all be made alive.

This is also the text (remember it's one of the earliest, written 20 or so years from Jesus' crucifixion) that asserts the Resurrection to be critical to the Christian faith:

1 Corinthians 15:17-19 (ESV)
¹⁷ And if Christ has not been raised, your faith is futile and you are still in your sins. ¹⁸ Then those also who have fallen asleep in Christ have perished. ¹⁹ If in Christ we have hope in this life only, we are of all people most to be pitied.

If anything, the Gospels, which were written later, downplay the Resurrection by giving us more details about Jesus' earthly ministry. Mark even ends immediately after the women's discovery of the empty tomb and doesn't provide a post-Resurrection account. (Whether this was by design or was a historical accident is not known.)

Reference: I draw most of my information from N. T. Wright's The Resurrection of the Son of God, which stands alone as the best survey of the history of the idea of the Resurrection ever written. If I don't stop now, I'm in danger of summarizing his entire book.