Obviously in western culture that evolved subsequent to the printing press easy publishing has become critical to how we live our modern lives and it's easy to draw a line connecting those dots, but it does not necessarily follow that the printing press either triggers or is a prerequisite for industrialization.
Even if the printing press was a major contributor to Europe's rise, that's not quite the same thing as the Ottoman's decline. Europe was eventually in a position to deal a deathblow but the Ottoman Empire had a lot of issues for a long time prior to its end (which coincided with several European empires as well). Perhaps the printing press could have helped some of these issues, but it's not at all clear it would have done more good than harm.