Well, it seems not
Scholars like Nöldeke believed that the Qur’an was wholly authentic, without any interpolation - "Keine Fälschung; der Qur’an enthält nur echte Stücke" - were obliged to revise their opinion and admit without restriction the possibility of interpolations ("Ich stimme aber mit Fischer darin überein, dass die Möglichkeit von Interpolationen im Qoran unbedingt zugegeben werden muss"). According to Muslim writers: The first historical data about the collection of the Qur’an have come down to us by the way of oral Hadith, and not of history. This is very unfortunate; because a critic is thrown into that medley and compact body of legends, true or false, genuine or spurious, which began to receive unchallenged credit at the time of the recrudescence of Islamic orthodoxy which gave birth to the intolerant Caliph Mutawakkil (AD 847-861).
The reader is thus astonished to find that the earliest record about the compilation of the Qur’an is transmitted by Ibn Sa'd (AD 844) and by the traditionists Bukhari (AD 870) and Muslim (AD 874). The most ancient writer, Ibn Sa'ad, has devoted in his tabaka a long chapter to an account of those of the "Companions" who had "collected" the Q in the time of the Prophet. He has preserved 10 contradictory traditions, in which he enumerates 10 different persons, each with a list more or less numerous of traditions in his favour; these persons are: 'Ubayy ibn Ka'b (with eleven traditions); Mu'adh (with ten traditions); Zaid ibn Thabit (with eight traditions); Abu Zaid (with seven traditions); Abud-Darda (with six traditions); Tamimud-Dari (with three traditions); Sa'ad ibn 'Ubaid (with two traditions); 'Ubadah ibnus Samit (with two traditions); Abu Ayyub (with two traditions); 'Uthman ibn 'Affan (with two traditions).
On pp 113 another curious addition informs us that it was 'Uthman ibn 'Affan who collected the Qur'an under the Caliphate of 'Umar, and, therefore, not in the time of the Prophet (did Uthman forget that already Abu Bakr had ordered to Thabit to write down the Qur’an, and that it was held by Hafsa?)…..strange indeed
Another tradition reported by the same author, already noticed by Nöldeke, attributes the collection of the Qur’an in suhufs to the caliph 'Umar himself.
The second in date, but the most important, Muslim traditionist; Bukhari, has a very different account in connection with the collectors of the Qur’an in the time of the Prophet. According to one tradition which he reports, these collectors were four Helpers: 'Ubayy ibn Ka'b, Mu'adh ibn Jabal, Zaid ibn Thabit, Abu Zaid. According to another tradition they were: Abud-Darda, Mu' adh ibn Jabal, Zaid ibn Thabit, Abu Zaid.
Most historians however (Nöldeke as well), endorse the famous tradition that the Qur’an was collected in the time of Abu Bakr, and not in the time of the Prophet: This is the oral record which, appearing 238 years after the Muhammad's death, was accepted as true and authentic, by the most eminent Orientalists of the last century, led by Nöldeke.
Why we should prefer these two traditions to the great number of the above traditions sanctioned by Ibn Sa'd, an author anterior by twenty-six years to Bukhari, is puzzling. Nöldeke, however, believes that Bukhari is right and Ibn Sa'd wrong, because if the Qur’an was collected in the time of the Prophet, why should people have taken such trouble to collect it after his death? But the question is, why should we prefer at all the story of Bukhari to that of Ibn Sa'd who is at least credited with priority of time? What should we do then with the other two traditions of Bukhari which are in harmony with Ibn Sa'd in assigning the collection of the Qur'an to the lifetime of the Prophet? What, too, should we make of the tradition reported by Ibn Sa'd to the effect that the Qur’an was collected by 'Uthman b. 'Affan alone, under the caliphate of 'Umar? The historian Tabari has another account:
"'Ali b. Abi Talib, and 'Uthman b. 'Affan wrote the Revelation to the Prophet; but in their absence it was 'Ubayy b. Ka'b and Zaid b. Thabit who wrote it." He informs us, too, that people said to 'Uthman: "The Qur'an was in many books, and thou discredited them all but one"; and after Muhammad's death, "People gave him as successor Abu Bakr, who in his turn was succeeded by 'Umar; and both of them acted according to the Book and the Sunnah of the Apostle of God - and praise be to God the Lord of the worlds; then people elected 'Uthman b. 'Affan who ... tore up the Book."
A second series of traditions attributes a kind of collection (Jam') of the Qur’an to the Umayyad Caliph 'Abdul Malik b. Marwan (AD 684-704) and to his famous lieutenant Hajjaj b. Yusuf. A study of Shi' ah books reveals also some variants derived from the recension of 'Ali's disciples. The Qur’an could be have written down by d'al Hajjaj, who could have taken it out by a “prototype” detained by Uthman (this is the opinion of the famous Alphonse Mingana).
Summa summarum: there are thus three main theories about the collection of the Qur’an after the death of Muhammad, done by 1) Abu Bakr (632-34), who charged Zaid ibn Thabit to collect the fragments 2) Uthman (644-56) that, concerned about the differences in the MS, let (again Thabit) write down a standard version 3) al-Hajjaj (Governor of Iraq at the time of the Umayyad Abd-al-Malik (685-705)): who homogenized the orthography. It seems that the “tradition” tried to create a fictive past (taking in the Archangel Gabriel). In fact, Gabriel is much more present in the post-Qur’anic tradition, but almost absent in the Qur’an (only three citations in late Surahs).
Having standardized the final version, and having burnt all other copies, left the scholars in a situation where they cannot reconstruct the original Qur’an. That’s quite different from the very abundant availability of MS for the Bible. We cannot underestimate how important this is…in fact: we are unable to take advantage from some points like the one pointed out by Sahih Muslim, where he says that a whole Surah is missing (Muslim 2283-86)
More on that: here