No, The Crucifixion is not supported by established history or consensus among the Christians. They believe in it because of the traditions narrated later by St. Paul’s school of thought.
Imam Amin Ahsan Islahi writes about this: “neither did any incident of killing the Messiah nor of crucifying him took place but the followers among Christians of Saint Paul got hold of this cooked up story and authored a whole mythology on its basis and in this manner in order to please others harmed their own selves. (Amin Ahsan Islahi, Tadabbur-i Qur’an, vol. 2, 420)
… It is thus a fact that about the nature of the incident itself Christians … greatly differ with one another, and the mythology they have fashioned out has many discrepancies. These discrepancies are the obvious outcome of the fact that they have based their version and its reasoning on conjecture instead of reality, and in this manner the Christians crucified themselves on the cross from which the Almighty saved Jesus (sws). (Amin Ahsan Islahi, Tadabbur-i Qur’an, vol. 2, 421)
Also, Gospel of Barnabas stands in stark opposition to their view as narrated by Ghamidi sahib in Al-Bayan: “the situation that was created made the Jews believe that they had actually crucified Jesus (sws). What then did actually happen? The most likely of scenarios is the one depicted in the Gospel of Barnabas. As per its account, when Judas Iscariot after being bribed by the chief priest of the Jews came over with some guards to arrest Jesus (sws), four angels at the behest of the Almighty took him away and transformed the voice and face of Judas into exactly those of Jesus (sws). It was he who was crucified. No one was able to even touch Jesus (sws). It is while pointing to this scenario that perhaps the Qur’an has dubbed it as being made muddled up for the Jews.”