"Replacement Theology" is a perjorative term created by Dispensationalists as a misnomer for Covenant Theology. There is no "replacement" of Israel with the Church in Covenant Theology, that is a myth created by Dispensationalists. In Covenant Theology Israel is not "replaced", it's expanded to include Jews and Gentiles.
To answer the original question- Does Islam improve Christianity? A simple comparison will do.
Jesus commanded us to love our neighbors-Islam gives room to kill our neighbors if they don't or won't believe in Islam
Through Christianity we can enter heaven by having a relationship with Jesus-through Islam we can only get into heaven by good deeds(murdering is not a good deed regardless of who you are).
Christianity is true-Islam is false.
Jesus is the son of God-not a prophet
Also here's something else to think about- Christ means "the annointed one", if Islam is true then why would someone who is annointed not be able to complete his mission? He wouldn't.
(the final answer to the original question is NO)