I was just reading about these mystery religions on wikipedia, and apparently they were popular among Greeks and Romans in the early centuries CE. Wiki cites reasons for their popularity such as systematic doctrine, mystical experience, and a sense of community.
From a naive perspective (mine) Christianity seems to satisfy these same criteria. It's also foreign, like the cults of Osiris and Mithra. The existence of early Christian Gnostic sects seems to corroborate the connection to me.
Yes - to an extent. Christianity and the cults of Mithras and Isis (Osiris) all share common themes, especially resurrection of a divine human.
However, Christianity stems from Judaism, which at the time was a niche religion practiced by only a small percentage of the population. Like Judaism, Christianity is monotheistic, and (please correct me if I am wrong) the only monotheistic religion in the Roman Empire. Thus, unlike other mystery cults, followers of Christianity could ONLY follow Christianity - the very nature and practice of polytheism in this period being that one could "pick and choose" which gods to worship, with the underlying assumption that all gods were valid.
So yes, while Christianity does share themes and a certain exotic-ness with the mystery cults, it's monotheistic nature limited initial popularity.