The answer is affirmative. Yes, Christianity is possible without, not only the Old Testament, but also without the New Testament. As a matter of fact, so is true for Judaism – it is also possible without the Tora/Tanach/Talmud.
On any minimally advanced stage, both of them do not, and should not, read these barbaric, simplistic books literally. This is what Christian Church Fathers and Judaic Thinkers were talking all along. This books must be, or, we say, may be, taken as an inspiration for the intelligent, spiritual, interpretive reading.
Though, the same, identical reading may be achieved if we take any significant corpus of a talented, sophisticated literature, say, the Classic one, the Mahabharata, or a good Contemporary one.