No. Christianity would not exist without humans
Any religio (from whence the word religion derives) cannot exist without humans. Definitionally speaking, a religio is literally "the way" meaning the way in which a human acts on a regular basis. Under that definition, all people - even atheists - have religions. It is simply their way of being in the world. Some religions require regular ritual practices like praying, studying, or visiting the temple/high place of worship/shopping mall, others ways of believing, and still more ways of interacting with their fellow man.
Christianity, is a religio which focuses on comporting oneself in Christ. It involves living through him and following him. Indeed, originally, Christians were called "the Way" and "followers of Christ." To Follow inherently requires a follower and a followee. Absent these things, there is no following, and hence no Christianity.
For many Christians, raised in an anti-Pharisee mindset, this is a good thing. We eschew ritual and focus on relationship. We seek to worship in spirit and Truth. We have no love of ritual per se, but rather the object of our affection. Absent one to enjoy that relationship, indeed, Christianity ceases to exist.
Yes, God would still continue to exist without his creation
That said, Christians believe that God is a non-contingent being. IN other words, God's existence cannot depend on his creation. It is ultimately a strange irreducable distinction - leading many theologians to even consider it a false dichotomy, but the point is simple enough - an omnipotent God does not derive his existence from his worshippers - rather he created them. Any other action disregards both his omnipotence, and simple causation.
Biblically speaking, Christians believe that "In the beginning, God". That simply means that God did exist for a long time without followers. THe concept of redemption - re-calling his Creation back to him necessitates that.
As such, no, the religion may not exist absent followers, but that does not mean that God himself does not.