I am going to say that no, the original NT could not have been Aramaic. Why? Because the NT in Greek quotes quite a fe3w times from Aramaic, then translates the Aramaic word or phrase. Thus, if we recognize those Aramaic quotations as Scripture (and we do, right?), then the NT was originally written in Greek.
The prime example is the statement of Jesus on the cross: "And about the ninth hour Jesus cried with a loud voice, saying, Eli, Eli, lama sabachthani? that is to say, My God, my God, why hast thou forsaken me?" (Matt. 27:46).