In that Islam is a twisted form of the Catholic heresy we name Arianism, yes, they have a common heritage. Islam is a heretical religious system that derives from Catholic heretics.
After the Arian heresy was mostly resolved, instead of executing the heretics, many of them were exiled to the deserts of Arabia, where, by and by, this stupid camel trader named Mo came across them and learned their demonic doctrines.
If the Church had punished these heretics properly in the first place, Islam may have never happened.
Goes way, way back, to the time of Sarah and Hagar, Ishamel and Issac.