That seems very unlikely to me. The Muslim world is less industrialized. The Ottomans were making a good start, but they were making a good start in Istanbul/Constantinople, which is on the wrong side of the Bosphorus and has been removed from the world. The Ottomans may no longer have a navy if it was stationed in the wrong place and they lost AFAIK their only military shipyard and with it everyone who knows how to design or build an ironclad. Not so the US. This compounds the coal problem. Oil isn't yet a major fuel and the only working coal mine in the Moslem world is in Sumatra, run by the Dutch, and has only been in operation for a couple years. If they make a run for Australia or America or possibly even Japan there's not expertise to start mining Europe's coal under Moslem control. I'm not sure how much of a merchant marine they have or can grab to get itYep and in a few centuries if it can get a strong central government under a single rule, it will by default become a hyperpower as America exhausts itself.
Shipbuilding is not as far advanced in New South Wales or Japan as it is in the US, but it exists and I don't think any of the Muslim nations have any to speak of with the loss of Constantinople.
This lack of coal will bring what industrialization hasn't vanished with Constantinople to a screeching halt until they acquire a source presumably by conquering India which will take time giving Japan and Australia a head start and the US time to further its head start. America won't exhaust itself for well over a century. North America isn't that much less virgin than Europe and it's a lot larger.