Lot of interesting stuff in this thread, really.
Some points:
There WERE religious-grounded objections to printing press as such in the Ottoman Empire IOTL, though they were not universal.
The structure of Islamic learning, especially but not exclusively in that era, was quite intimately intertwined with handwriting. Learning something was quite often connected with copying it, though this connection was far from absolute or universal.
The very nature of Arabic script, as it was used to write Arabic, but also (to a lesser extent) Persian and Turkish, was rather conducive to such situation. However, potential for printing existed. Now, a century before Gutenberg was hardly the best time for it, especially as far as the Ottomans go. The Ottomans domains in 1353 were a peripheral relative backwater in the Muslim world, and the worst effects of both the Mongol conquest and the waves of Black Death were quite active. Poltically, it was a time of weakness, decline and instability for most Muslim polities west of India, with the Mamluk state as the most remarkable exception.
Someone pointed out that the Kufic script is better suited to printing than the subsequent various forms of naskhi, which is basically true, but this would require an invention of printing press way earlier, before 1100 AD at latest I think.
I would not rule out, but it makes for a very different scenario (one where Europe is likely to pick it out in the thirteenth century, for example).
It is really a complex thing.