The Egyptian language manages to survive the Arab conquest. Would this ultimately weaken Islam? How does Egypt relate to other Muslim countries both is medieval and modern times?
It's hard to see Coptic thriving in a wider Muslim world where Arab tribes are moving around, and the language of war, high culture and administration, and, above all, of Revelation, is Arabic.
Having said that the language of the Egyptian fellaheen (peasants) in the Nile Valley was stubbornly Coptic for several centuries after the 7th century Arab Conquests.
So could it survive? Yes. But something would need to give Coptic cultural protection, e.g. at the very least an independent, self-consciously Egyptian state, which does not consider itself a part of the wider Arab world.
Would it weaken Islam? Depends what you mean. If Egypt holds out, so too do all north African territories further west. Could a Caliphate minus Egypt and the west survive and thrive? Yes of course. But if this independent (Christian?) Egypt is trying to hold out against the powerful Caliphate it will need some powerful allies if it is not to go under at some point. And it
would be attacked alot by Muslims: Egypt is just too close for comfort to key trade routes and the Holy Cities themselves...
How did Egypt relate to other Muslim countries? Sometimes well, sometimes not so well. But it always was (and is) a major part of the Muslim world IOTL. Hence Barak Obama making it the first Muslim country he visited after becoming President of the USA...