Nothing about the conversion to Christianity turned out well for Rome or the rest of western culture. Almost the entirety of Greco-Roman learning was suppressed and forgotten for a thousand years as western Europe endured the dark ages under the anti-science catholic church. Progress was rejected for a millennium of holy wars, inquisitions, superstition and stagnation.
It did all of that, no argument, but it also led to the Western ideology that we now embrace as the best that we have created to date.
If Islam were to take over, learning will again be suppressed and forgotten and their own Inquisitions and Jihads will be the order of that horrible day.
Regards
DL
Our western ideology is based in Rome but the best of it was the result of the reformation and the renaissance. That is where ideals of freedom of thought, humanitarianism, science and rationality became the cornerstone of our civilization.
I do not fear Islam taking over, it may take another hundred years but it will be rendered toothless or be destroyed like everything else that has challenged western civilization.