Has the Catholic Church responded to the apparent implausibility of a census as described in Luke?

No, the Catholic church has not provided an official response or explanation for the apparent implausibility of the census as described in the Gospel of Luke.

While the above text suffices as a strict answer to the question, I will provide my personal response to the apparent implausibility. It has two parts: first, what Luke meant by mentioning Quirinius census, and second, in response to what census (hint: not Quirinius') Mary and Joseph travelled to Bethlehem.

1. Getting right at long last the reason why Luke mentions Quirinius' census

A correct interpretation of Luke 2:2 requires taking into account a key item of historical information of a most practical nature: any census of subjects (as opposed to citizens) of the Roman Empire was carried out for tax purposes, to determine the taxable base of each subject. In such a census, people to be registered were not expected to travel but to do exactly the opposite: stay in their homes and wait for the census officer, who was above all a tax assessor. Flavius Josephus, in his description of precisely the census ordered by Quirinius in 6 AD, explicitely states that the registered people had their possessions assessed (AJ 18.1.1 and 18.2.1). And it is evident that Joseph did not have properties in Bethlehem, otherwise he and Mary would not have had to seek shelter in a manger for Mary to give birth.

"1. NOW Cyrenius, a Roman senator, and one who had gone through other magistracies, and had passed through them till he had been consul, and one who, on other accounts, was of great dignity, came at this time into Syria, with a few others, being sent by Caesar to he a judge of that nation, and to take an account of their substance. Coponius also, a man of the equestrian order, was sent together with him, to have the supreme power over the Jews. Moreover, Cyrenius came himself into Judea, which was now added to the province of Syria, to take an account of their substance, and to dispose of Archelaus's money; but the Jews, although at the beginning they took the report of a taxation heinously, yet did they leave off any further opposition to it, by the persuasion of Joazar, who was the son of Beethus, and high priest; so they, being over-pesuaded by Joazar's words, gave an account of their estates, without any dispute about it. Yet was there one Judas, a Gaulonite, (1) of a city whose name was Gamala, who, taking with him Sadduc, (2) a Pharisee, became zealous to draw them to a revolt, who both said that this taxation was no better than an introduction to slavery, and exhorted the nation to assert their liberty;" (AJ 18.1.1) [1]

"1. WHEN Cyrenius had now disposed of Archelaus's money, and when the taxings were come to a conclusion, which were made in the thirty-seventh year of Caesar's victory over Antony at Actium, he deprived Joazar of the high priesthood, which dignity had been conferred on him by the multitude, and he appointed Ananus, the son of Seth, to be high priest;" (AJ 18.2.1) [1]

Therefore, the historically informed translation of Luke 2:2: "hautē apographē prōtē egeneto hēgemoneuontos tēs Syrias Kyrēniou" is "this registration took place before Quirinius was governing Syria". Note that rendering "prōtē" as "before" is consistent with the established translation of the end of Jn 1:15: "hoti prōtos mou ēn" = "because He was before me".

Thus, noting from Acts 5:37 that Luke was fully aware of the event of Quirinius' census, its nature and its consequence, namely the uprising of Judas the Galilean, the reason of his mentioning the event in Luke 2:2 becomes crystal clear: state for the record that he was not talking about that census. I.e., Luke is saying: "Given that in a Roman census of imperial subjects for taxation purposes people must remain at their homes (a fact which is well-known by everyone in my time but will have been long forgotten by the XXI century), I state for the record that the census that prompted Joseph and Mary to travel to Bethlehem was before Quirinius ordered his infamous one."

How then could it come to pass that Luke's statement was interpreted for centuries in exactly the opposite way as he meant it? Because of complete unawareness of historical context. I imagine that anyone living in the Roman Empire at that time would find this discussion hilarious to the point of ridiculous, and think: "How can these guys not understand that a census of subjects of the Empire (as opposed to Roman citizens) is for tax purposes, and that people must wait for the census officer at their homes? How else could the census officer reckon the taxable base of each person other than by having a look at his property?"

2. What then was the relevant census that prompted Mary and Joseph to travel?

The census that prompted the travel of Joseph and Mary was ordered by Herod and obviously restricted to the territory ruled by him. It approximately coincided in time with a global census ordered by Augustus in 8 bC, but was of different nature. Whereas Augustus' 8 BC global census was restricted to Roman citizens and for statistics, not tax, purposes [2], the motive of the Census ordered by Herod in 7/6 BC was that all his subjects should swear fidelity to Caesar and the king (AJ 17.2.4) [4].

"These are those that are called the sect of the Pharisees, who were in a capacity of greatly opposing kings. A cunning sect they were, and soon elevated to a pitch of open fighting and doing mischief. Accordingly, when all the people of the Jews gave assurance of their good-will to Caesar, and to the king's government, these very men did not swear, being above six thousand;" (AJ 17.2.4) [3]

Together with the record of the oath, people were registered for an egalitarian contribution per capita in the way ordered by Ex 30:11-16, in which the possessions of each person were not taken into account.

In the context of a registration ordered by Herod, and knowing his profile, the order that all descendants of King David should register in one place was wholly plausible and logical, as it allowed Herod to know all potential claimers to the throne of Israel (and hence potential threats to his position). Furthermore, it is highly likely that the duty to travel to the city of their ancestors was in force only to King David's descendants, because of the people in general Luke says that "all went to be registered, each to his own town" (Lk 2:3), not "each to the town of his ancestors".

References

[1] https://www.ccel.org/j/josephus/works/ant-18.htm

[2] Res Gestae Divi Avgvsti Chapter 22 (The Deeds of Divine Augustus) translated by Thomas Bushnell, BSG. Available online at: http://classics.mit.edu/Augustus/deeds.html#71

[3] https://www.ccel.org/j/josephus/works/ant-17.htm

[4] Armand Puig i Tàrrech, "Jesus: An Uncommon Journey : Studies on the Historical Jesus", Mohr Siebeck, 2010. Chapter 2 "The Birth of Jesus", Section 4 "A More Judaico Census Decreed by Herod", pp 74-84. Partially available online at: http://books.google.com/books?id=elFp5tRSUH0C

The matter of which census Luke referred to requires knowing the year Jesus was born. The Bible does not specify which year and problems with this are written about in the ‘Concise Sacramentum Mundi Encyclopedia of Theology’ (1981) edited by renowned Catholic Professor Carl Rahner. On page 732 Catholic scholars Ingrid Maisch and Anton Vogtle write:

The year of Jesus’ birth is also uncertain. The difficulties can only be briefly indicated: Jesus is said to have been born under Herod the Great when Quirinius was governor of Syria (Lk 2:1). But there is no evidence that Quirinius was governor during Herod’s lifetime. None of the explanations of this contradiction so far suggested is satisfactory. All that is generally accepted is that Jesus was born before 4 B.C. (death of Herod). More precise details cannot be drawn from the infancy narratives of Matthew and Luke.

However, there are biblical clues about when John the Baptist was born, which is significant because John was six months older than Jesus. See http://taylormarshall.com/2012/12/yes-christ-was-really-born-on-december.html for Catholic reasons for a 25 December birth, based on their view that John the Baptist was born in the summer (argued for further down the article). Some Protestants argue for him having a spring birth, meaning Jesus would have been born around September/October and conceived the previous December but either way, they fit in with the 7 B.C. census theory which now follows.

The year 7 B.C. was a rare one in having a triple conjunction of Jupiter and Saturn, which could fit in with the account of Magi from Persia seeing a significant star. David Hughes, Professor of Astronomy at Sheffield University, discovered that, three years before Herod's death, there was a rare series of alignments of Jupiter and Saturn. They came together three times over several months. The first conjunction was in May, he said, giving them plenty time to plot the next two conjunctions (in September and November) and travel the very long distance to Jerusalem, over which the second conjunction appeared at the time of Jesus' birth. Herod the Great summoned Jewish religious experts who told him and the Magi that a prophesied King would be born in Bethlehem. By the time the third conjunction happened, it brought the Magi to Bethlehem, to the very house where Mary and the child were. This implies a bit of a time lapse between Jesus' actual birth in a stable and being a child in a house in Bethlehem. Clearly, the stable accommodation had only been temporary (undoubtedly much to Mary’s relief). The Bible shows that Mary and Joseph stayed local as Jesus was circumcised on his eighth day in the temple, and Mary went to the temple for her purification.

Zoroastrian Magi viewed Jupiter as representing a new king; Saturn the old. The planets coming together would signify a change of ruler. This happening in Pisces would speak to them of Israel as they associated Pisces with Israel. This triple conjunction would make the planets involved appear to be travelling backwards and, on specific days, to have actually stopped. All planets do this, but it is very rare when two do so at the same time. This accounts for a special light appearing to stand still over Bethlehem in November that year. Thus goes the explanation according to Professor David Hughes. I have no idea if he is a Catholic or not, or even if he has any religious faith, but he claims his theory is based on cosmological events. An article on this was in 1 September 2009 ‘Weekend’ magazine which was reviewing a BBC2 documentary on Christmas Eve that year. Now, here comes the link to Luke’s census.

There was a census in 7B.C., written about by 5th century historian Orosius. He said Augustus ordered a census of each province everywhere, with all men to be enrolled to show allegiance to Caesar Augustus. Josephus notes that "When all the people of the Jews gave assurance of this goodwill to Caesar, and to the king's government, these very men [the Jewish Pharisees] did not swear, being about six thousand." This census took place in 7 B.C. and was for non-Romans. Romans wouldn't need to be registered as showing allegiance to Caesar but Joseph would need to be registered, which accounts for him taking Mary to Bethlehem where he'd been born. That census mentioned by Orosius could have been that little known one Luke referred to, for Jewish men to swear allegiance to Augustus, which the Pharisees refused to do. It seems to have been for non-Romans, to boost Augustus's inflated ego and calm his nerves about disloyalty. The vanity of the Roman emperors knew no bounds and they would not care how much money was spent / lost in demanding people sign up to their rules. The wealth of Rome was fabulous. A census was nothing to them. Besides, it was the poor people forced to travel who would lose out and since when did Rome ever care about poor people?

http://en.wikipedia.org/wiki/Census_of_Quirinius supposes Luke’s account is wrong but then gives information on Quirinius’ later rule and the later census. Official Catholic views on this triple conjunction happening the same year as this little-known census mentioned by Orosius have not come to light in my research.