As others have noted, that didn't stop Ottoman Turkish (which is unintelligible with Standard Turkish) from becoming the official language OTL, nor did it stop Persian from becoming official in the non-Persian majority Mughal Empire, nor did that stop Turkish from being the language of court in the Arab-majority Khedivate of Egypt...among dozens of other examples. For most of the time period that we're looking at, demographics don't play as big of a role in what the official language is as one might expect. It's also archaic for most of the history of the Ottoman Empire to look at it through the lens of linguistic nationalism when in fact it is often defined as a Persianate society despite having a relatively small Iranian population.
Instead it's more valuable to look at factors such as prestige and what language the ruling class prefers, which can more accurately explain OTL official language trends. So in order to make Arabic the official language of the ruling class, you either have to make Arabic prestigious enough that non-Arab ruling classes prefer to use it, as was the case with Persianate societies OTL, or introduce enough Arabs into the ruling class of the empire (and somehow prevent them from linguistically assimilating) that Arabic becomes the dominant language of the ruling class and thus of the empire. It's probably easier to increase the prestige of Arabic, perhaps by amplifying the cultural influence generated in Cairo by the Mamluks OTL; but then there's the issue of introducing that language to Ottoman elites. By the time you can speak about the Ottomans as an existing state, Persian has been the prestige language of Anatolian beylik elites since the Sultanate of Rum. Historically the Ottomans did end up abandoning Persian as the language of court, but only in favor of a very highly Persian-influenced language (Ottoman Turkish). So introducing Arabic as an official language would probably require similar circumstances to the OTL abandonment of Persian, such as a strong rivalry with a Persophone state, as well as additional factors like a stronger Arabic literary/poetic tradition that would allow it to replace Persian where Ottoman Turkish did OTL.
In terms of how this would affect the empire, I would say that while Arabic would become the lingua franca of the empire, OTL not that many people spoke Ottoman Turkish, as shown by how quickly it died with the Ottoman Empire, so I don't think that many people would end up speaking Arabic in this ATL. However, if nationalism does develop similarly to OTL (which isn't necessarily inevitable) then instead of the revival of Arab consciousness that happened OTL, we might see a revival of Turkish identity and possibly even Turkish separatism.
