I don't think that's true. Pre-modern demographics are hard to estimate, especially subtle social changes like religious conversion and change. The best estimates we have about conversion to Islam in the wake of the early Arab conquests is Conversion to Islam in the Medieval Period: An Essay in Quantitative History by Richard W. Bulliet. It's expensive to buy, but many universities will have it accessible as an electronic resource (also, any decent library will have it as a print resource).

His methodology examines all the names in the written record, and where they're from, and attempts to come up with an estimate of population size based on that. As you can guess, this relies on several assumptions and has relatively wide margins of errors. However, everyone agrees this is also the best work that's been done on the question and provides the more or less consensus answers. This website (which I haven't more than glanced at) looks like a decent summary of Bulliet's argument [edit: read this whole thing, I'll leave this link up so that you can see all the charts, but the guy's overall thrust and conclusion, I think, are empirically just wrong. The use is in the citations from other works; I don't think the analysis or conclusions are insightful or even, in places, factual]. More importantly, it reproduces some of Bulliet's graphs (not all of them though--I also made an imgur album with a slightly different selection of charts, but I can't find it now). Anyway, here's Bulliet's estimate for Egypt and Tunisia (he combines them together in his analysis). Notice that Bulliet estimates the population is half Muslim ~890 CE, and around 90% Muslim ~1050 CE. The Ottoman Dynasty is only founded in 1299 CE, and only conquers Egypt in 1517, at which point it has already been Muslim majority for half a millennium.

Now, this is about population, rather than culture, and I don't know enough about the Early Modern Arab World to comment on any cultural changes the Ottomans may have brought. But somehow, I doubt it. A lot of nationalist historiography in the Arab world has a tendency to look at the Ottomans as the origins of what's wrong with society, and to construct a narrative of "we were free and brave and good, then we were oppressed under the Ottoman yoke, then we established independence again." That's a narrative common to nationalist movements everywhere (you can write Finnish nationalist history by substituting "Russian yoke", or Hungarian nationalist history by adding in "and the Hapsburg yoke", etc.), but yeah, I don't think that's possible. Especially since the Ottomans weren't Arabs, and Muslim Arabs conquered (and ruled) Egypt hundreds and hundreds of years before the Ottomans came.