Of course it does, unless we're going to say that Jesus is indeed about the eternal principles involved (Christianity = "be nice" in some form) rather than the specific events of his life, death, and resurrection. If the historical event of the crucifixion and resurrection are not critical to Christianity, then it is just another non-historical religion teaching people how to get to God, rather than God taking on human flesh and giving his life for his beloved creation.
So the historicity matters. But what about the accuracy of small details along the way? The issue is trust. Can you trust what the Bible says?
This is not idle speculation, for hard on the heels of Caesar Augustus and his proclamation that all the world should be enrolled we find a difficult turn of phrase. Normally this would be a straightforward verse to translate; all the most popular English translations include some form of the words, "This was the first enrollment, and took place when Quirinius was governor of Syria." We've heard it on Christmas Eve over and over again.
The problem is that if Luke 1:5 is accurate, and if Matthew's account involving Herod the Great is accurate, we have a problem. Because Herod the Great died in 4 BC, while Quirinius didn't become governor of Syria until 6 AD. There was indeed a well documented census in 6-7 AD (Luke even refers to it in Acts 5:37) but if we believe this is the census mentioned in Luke 2, it creates other problems. (If you're looking for an in-depth discussion of the issues, here is a good summary.)
There was also a census in 8 BC that might serve our needs nicely, but Quirinius wasn't governor at that time. Some have suggested that perhaps Quirinius oversaw the census and only later was appointed governor, and that Luke simply identifies him by the title he had later, since that is the way people knew him. Others believe that Quirinius served twice as governor, once during the reign of Herod and later during the census of 6-7 AD. Still others -- and Wikipedia is quick to point out this option -- say that Luke just got it wrong.
What difference does it make?
I'm always hesitant to say that the Bible is mistaken. Not just because I want it to be accurate. Let me offer a couple examples, specifically from Luke. In Luke 3:1-5, Luke lists a whole array of rulers. He's obviously anchoring his story firmly in history. The trouble is, Lysanias whom we know from the writings of Josephus did not serve as tetrarch of Abilene while all these other rulers were in power. He was executed by Mark Antony about 70 years earlier. So for a long time it was considered a simple fact that Luke made a mistake. Then an inscription was found dating to the reign of Tiberius, the correct time, referring to Lysanias, the tetrarch of Abilene. Apparently there was a second Lysanias, perhaps a son who inherited part of his father's lands, and governed precisely during the time when these other rulers were in power. Luke had it right. (See this article which includes a nice summary of this issue.)
Another example: In Acts 17:1-9 we read the story of Paul and his companions in Thessalonica. Luke uses a term for the city officials here -- in Greek, "politarchs." For years scholars made fun of Luke for making up a word. No other reference was known in any of the Greek-speaking world to an official called a "politarch." Scholars thought it was like a kindergartner making up words, since it is a simple cobbling together of "polis" or "city" and "archus" or "ruler," thus, "city-ruler" or city official, as the NIV has it. Luke obviously had no first hand knowledge of Thessalonica and just made up what he thought was an official sounding term. Then archaeologists found an inscription over the gateway into the city (Thessaloniki in modern Greece) that listed the names of the -- you guessed it -- politarchs. This is a term that was apparently not used in the rest of the empire but was specific to this community, and Luke uses it exactly right.
So I'm hesitant to say Luke is wrong about Quirinius, because he's been right before when all modern scholars were convinced he was wrong.
Does it matter? Maybe not. Even if Luke was wrong about Quirinius, it wouldn't change the overall historical reliability of the Bible. But what is our assumption? Modern scholars have been trained from their earliest days to treat the Bible as great mythology, but lousy history. Is this a reasonable assumption for scholars to bring to their work? More important, is this a good assumption for a follower of Jesus to carry?
On Christmas Eve when I hear Luke 2 read, I don't think I'll be wrestling with the problem of Quirinius. Instead I'll be marveling at the way God set the whole business up so that Jesus could be born. But when the candles are extinguished and the last strains of Silent Night have faded, when the fluorescent lights come on and our rationality reasserts itself, it's nice to be able to trust that even if I don't know the answers to the problems in Luke 2:2, there's a good chance that someone will find a document, or an inscription, or a historical record of some sort and a hundred years from now Bible teachers will be saying, "Scholars used to think that Luke just made a mistake in describing the census under Quirinius, but now we know ..."