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. 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) 
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 , 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) .
"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) 
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".
 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
 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: