It is commonly believed that Hazrat Isa (as) would descend, all Christians would be converted to Islam. Let us analyze this viewpoint in light of Quran.
Quran states: “when Allah said, "O Jesus, indeed I will take you and raise you to Myself and purify you from those who disbelieve and make those who follow you superior to those who disbelieve until the Day of Resurrection. After that to Me is your return, and I will judge between you concerning that in which you used to differ” (al-imran-55).
From this verse, it is evident that nations following Hazrat Isa (as) would be always superior to those nations who do not believe in Hazrat Isa (as). It means Christian nations would always be superior to all non-Christian nations other than Muslim nations. [it may be noted that Muslims do have belief in Hazrat Isa(as)].
Another implication is that Christian nation and at least one non-Christian nation having NO FAITH in Hazrat Isa (as) would survive till 'Qiyamah'. Because Christians [ people following Hazrat Isa (as)] have been given superiority over non-Christians having no faith in Hazrat Isa (as) till 'qiyamah', it means Christians and non-Christians (non-Muslims) both would survive till Qiyamah. It means the concept that Christians would be converted to Islam after descending of Hazrat Isa (as) is not correct; in fact Christians would not believe in Hazrat Isa (as), when he would descend.
It is misunderstanding to believe that Christians would be converted to Islam after coming of Jesus (as). This misconception is based on al-nisa-159 which states:
" And there is not one of the followers of the Book but must certainly believe in this before his death, and on the day of resurrection he (Isa) shall be a witness against them". In this verse the word " layuminanna bihi" does not mean " to have believe in Jesus(as)"; rather it means "to believe in what Quran has stated about Jesus (as) in previous verses i.e. al-nisa-157-158.
Therefore we may conclude that Christians will not believe in Jesus (as) when he would descend. Most probably Christians would not believe in Jesus (as) because he will take side with the Muslims not with the Christians.