Wow, something I can actually discuss. This is my first time answering a post on Askhistorians, so I'll do my best and hopefully can edit if it gets flagged by the mods.

Before addressing the historical issue of the adoption of the printing press in regions where the Arabic alphabet is used, I'd like to briefly outline the actual technological aspects. By printing press I'm going to assume you mean specifically letterpress printing (the sort Gutenberg used) with moveable type, which is where the question of connected lettering gets interesting since as you you point out, each letter of the Arabic alphabet can vary its shape and design based on whether it is an initial, medial, or final letter. This might suggest that the issue of printing with Arabic alphabets was merely a matter of cutting more matrices (thing which are used to cast type) and casting more type. Viewed in this light, printing in Arabic might seem to just pose an economic concern or maybe one of practicality as opposed to technological capability. We should also note that Arabic, being an inherently cursive script, used ligatures, and lots of them. Ligatures are where two or even three letters combined to produce a slightly different letter shape. Like with the connected alphabet design inherent in Arabic, ligatures added to the numbers of type that would need to be cast. But Latin used ligatures too. This image reproduces Gutenberg's letter forms, a total of 292.

All that said, I don't want to dismiss the issue of the cost of producing type as a matter that printers were concerned about. At the end of the day, books were objects to be sold. Unlike scribes who produced manuscripts and received part of their commission upfront, a printer in the Early Modern period fronted the cost of producing a book (including paying all those people who set and align type, it was a complicated endeavor) and so a printer had to balance the risk of books not selling well to the cost that went into producing all these unsold books. So, cost mattered.

The 'invention' of printing with Arabic moveable type found its home in Italy in the 16th century. The first book is widely believed to be a devotional book of hours printed in 1514 in Fano (although people argue it's more likely it was printed in Venice), likely intended for Arabic-speaking Christians living in the Levant. A number of other books printed in Arabic appeared at this time in Italy, but the most organized and well funded efforts were around 1584 with the founding of the Medici Oriental Press in Rome (which later moved to Florence). Pope Gregory XIII even contributed to the press' establishment. A key element in why the books this press produced were much 'better' looking Arabic scripts, compared to previous efforts, lay in the skill of its typographer Robert Granjon, whose fonts we still use today. Granjon produced hundreds of ligatures, which together made a far more elegant, neater looking script. You can see a Google books scan of the press' version of Ibn Sina's Canon here. So for all intents and purposes, after the Medici Oriental Press, the issue of printing in Arabic was no longer a 'technological' matter so much as it was whether there was interest in these books. Presses in Leiden and England appeared not long after, some even borrowed the types that were made for the Medici Press in Rome. The question of why European scholars took an interest in learning Arabic again in the Early Modern period (don't forget the Medieval translation movements of the 10th - 12th centuries to translate Arabic works into Latin) is important to this issue of Arabic printing. I won't go into too much detail, but the combined effects of renewed interest in Arabic translations of classical Greek authors (and their Arab commentators like Ibn Rushd and Ibn Sina), the Catholic Church's efforts to reconnect with the Arabic speaking Christians I mentioned above, and the growing relevance of their Ottoman neighbors to the East (who spoke Turkish but also used Arabic for their scholarly productions) all led to a kind of second-wave interest in Arabic in the early modern period. I'll list some books below if you're interested.

Finally, as to the question of whether it 'delayed' the introduction of the printing presses in regions which used Arabic alphabets. I'm trained as an Ottomanist, so I'll focus on that region. As I've tried to suggest above, the technological difficulties of a connected, cursive language were overcome soon enough. The printing press wasn't delayed in being adopted beyond a specific European locale for any such technological reasons or for lack of awareness. The Ottomans were well aware of printing technologies. We read some of their criticisms as to its inaccuracies, and their distaste over it being possibly used to print Qur'ans. But Greek and Jewish communities living in Istanbul established printing presses much earlier than the first 'Ottoman' (by which we're insinuating 'Turkish' or 'Muslim') press founded by Ibrahim Muteferrika in 1729. The issue of why Ottomans did not adopt printing presses sooner, but did do so for other European technologies, is a complicated one that I don't personally think has been fully answered by the scholarship. One theory has to do with the strength of the scribal classes in opposing a technology that could threaten the means of their livelihood, but I think that's only partly there. I'm an Early Modernist so I won't wade into why printing presses were eventually established in places like Cairo in the 18th century, but I would caution you against viewing its adoption as a teleological necessity or as being 'late' compared to Europe. In my own work, I encounter Ottoman translations of European printed books all the time and its not seen as some novel thing, just an alternate form of textual transmission.

You can read a bit more about the early history of Arabic printing in Europe in my blog post here (with linked sources and more pictures).

Books:

The Republic of Arabic Letters by Alexander Bevilacqua

The 'Arabick' interest of the natural philosophers in seventeenth-century England edited by G. A. Russell (specifically the chapter by P. M. Holt "The Medici Oriental Press (Rome 1584-1614) And The Impact Of Its Arabic Publications On Northern Europe")

Success and Suppression: Arabic Sciences and Philosophy in the Renaissance by Dag Hasse

Eastern wisedome and learning : the study of Arabic in seventeenth-century England by Gerald Toomer

I can provide more books specifically about the Medici Printing Press but they're in Italian.

Article:

"The Enigma of the First Arabic Book Printed from Movable Type" by Miroslav Krek. Angela Nuovo has also written on it, but in Italian.