The short answer is no—the printing press was banned in much of the Islamic world for centuries after its adopting in the West. I've adapted the below from two previous answers I've written on the printing press & calligraphy in the Islamic world.

There were a number of factors that influenced the late adoption of the printing press in the Islamic Middle-East. I'm going to highlight three of these - cultural emphasis on calligraphy, the importance of clear "parentage" for works, and a fear that printers may change religious texts. Although I listed them separately, in reality these three factors often overlap and blend together.

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First I want to clear some misconceptions:

Printing is not incompatible with the Arabic script. Although the letters slightly vary in form depending on whether they start, are in the middle of, or end a word, there is nothing that stops Arabic from being printed. This is why, even though the printing press wasn't commonly employed in the Islamic world until the 19th century, Arabic printing presses had been used in Europe since the early 16th century. The first Qur'an was printed in 1537 in Venice, Italy and there was a large Arabic press that printed secular Arabic works in the Netherlands.

Nor was there some sort of Islamic bias against learning. The Islamic world produced advanced works on mathematics, astronomy, and medicine—especially prior to the European renaissance when the Islamic world often outpaced the Western world in scientific understanding—and had libraries with hundreds of thousands of manuscripts.

Having established those two facts, we can get into why the printing press did not cause the same revolution that it did in Europe.

Calligraphy was and remains a highly valued form of art in the Islamic world. Calligraphists took pride in their great skill in not only forming aesthetically pleasing letters, but also in providing elaborate illustrations and patterns to decorate important works, both religious and secular. Printing presses, especially early presses with their often crude lettering, could not hope to match the beauty of hand-written manuscripts. Nor could they match their accuracy.

A class of professional scribes and copyists - called warraqeen emerged from the 8th century. These warraqeen did not only reproduce works but also played a pivotal role in how accepted they were. Works were seen as authentic not only based upon what information they contained but also who that information was written by. James Redman links this to the Islamic idea of "definitive knowledge" or that "the perception of what could accurately be prescribed as truth, fact, or reality was dependent not upon abstract statements but rather who confirmed those accounts". The importance of chain of transmission can also be seen in other facets of the Islamic world, such as the isnad that records who passed down what hadith from the time of Muhammad onwards.

In his book Paper Before Print: The History and Impact of Paper in the Islamic World, Jonathan Bloom provides an explanation for how Islamic methods of reproducing manuscripts could have led to the production of many more books than pre-printing press Western methods. He highlights the impact of the oral tradition of Arabic and its necessity of ensuring a chain of transmission back to the original author, the "definitive knowledge" that Redman mentions. Bloom thus claims that the reproduction of books was not primarily a written venture but rather an oral one—the author would recite his work, often from memory, within a mosque. Scribes who were listening would then record what the author was dictating, creating an official copy of the work. For a manuscript to be considered an official translation, the scribe would have to read back the work to the author who would then certify that it is authentic and free from error. Bloom then adds that it was important to prove not only that a scribe heard a book from a specific source but also that he read it back to an approved source. With this double-layered verification, the chain of transmission was protected.

As arduous as this process may be, it has the definite advantage of ensuring that official reproductions are free from error and accurately portray what the author meant, a form of quality control if you may. Once a reproduction was certified as correct, it could then be read in other Mosques to circles of scribes to repeat the process. Bloom writes that

"in contrast to the situation in medieval Christendom, where a single scribe made a single parchment copy of the single parchment manuscript on the desk before him, one author in the Muslim world could generate a dozen copies from a single reading, and each of these authorized copies could generate another dozen. Within two 'generations' of readings, well over a hundred copies of a single work might be produced". (116)

He also mentions that authors could often also "double-down" and treat the recitation for quality control as another chance to have new scribes record the work, speeding up the process even more!

With printing, this chain of transmission was impossible to verify. Additionally, prints were difficult to check for their accuracy (and given the limited accuracy of many of the early European prints of the Qur'an, this fear may have been well founded). In Arabic, a single dot can change the sound of a letter, and thus the meaning of an entire word (for example, the letters "ra" (ر) and "za" (ز) were often confused in early Italian prints of the Qur'an.) Although printing gradually improved, even a few errors could fundamentally change the meaning of a text and put off Muslim scholars from accepting printing.

This fear of corruption in religious texts was one of the driving forces behind the Ottoman Sultan Bayezid II's 1485 ban on the use of printed books. As Muhsin Mahdi writes, one look at the early Qur'ans "must have made Muslim readers of the Koran think that only the Devil himself could have produced such an ugly and faulty version of their Holy Book".

The ban of Beyezid II was followed by a similar ban from Sultan Selim I in 1515. However, he allowed for dhimmis, or religious minorities such as Christians and Jews, to print books. These exceptions allowed the first Hebrew printing press in Constantinople to operate from the end of the 15th century, whereas the first Arabic printing press in the Ottoman Empire did not open until 1720 under the reign of Sultan Ahmed III, when a Hungarian convert to Islam named Ibrahim Muteferrika was enlisted. Despite the spread of presses in Anatolia and the Levant, it took even longer for printing to become common in areas like Egypt, which only developed a printing tradition following Napoleon's 1798 invasion.

Finally, I should note for the sake of completeness that some believe the Arab world developed printing much earlier, even earlier than the Europeans. Geoffrey Roper writes that there are allusions to printing in poetry as far back as the 10th and 14th century in Fatimid Egypt. He adds that early mass produced charms and amulets, bearing prints of the various holy names of God, were found surviving back to the 10th century, with more from the 13th to 16th centuries. However, if it did exist then, it was not widespread and was therefore not the revolution that you were looking for.

So, in sum, it was largely cultural factors that limited the acceptance of the Printing Press in the Middle East until the 19th century. Due to heavy reliance on knowing the chain of transmission for works as well as the necessity for ensuring the accuracy of copies—something harder to do on a printing press—it merely took longer for the printing presses to catch on in the Arab world.

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You'll see that I focused this answer on the question in your title, not the follow up in the post's body. But as a general aside, there already was a schism in Islam prior to the 15th century, no printing needed! Hope this helps.

Sources

Paper Before Print: The History and Impact of Paper in the Islamic World by Jonathan Bloom

"Commencement of Printing in the Muslim World: A View of Impact on Ulama at Early Phase of Islamic Moderate Trends" by Moinuddin Aqeel.

"Printing History in the Arabic-Speaking World" from the Yale University Library

"From Pen to Press: Debates on the Development of Islamic Printing" by Samuel Taylor

"Muslim Printing Before Gutenberg* by Dr. Geoffrey Roper