No, he isn't supposed to appear to Christians. The Bible says that many would come in the last days saying they were the Christ, and would appear as angels. Believers were warned to not pay any attention to the counterfeit Christs as they were demons masquerading as "Christ".
Not picking a fight here, just curious about your self-description. Saying you're a non-Christian is broad and ambiguous, to say the least. Why not identify what you are instead of that which you are not?
Let's see what the Book has to say...
First off, we have 3 accounts of Christ basicly saying "Goodbye" to His disciples - Christians, if you will...
Matthew 26:29
I tell you, I will not drink of this fruit of the vine from now on until that day when I drink it anew with you in my Father's kingdom."
24. "This is my blood of the covenant, which is poured out for many," he said to them.
25. "I tell you the truth, I will not drink again of the fruit of the vine until that day when I drink it anew in the kingdom of God."
17. After taking the cup, he gave thanks and said, "Take this and divide it among you.
18. For I tell you I will not drink again of the fruit of the vine until the kingdom of God comes."
19. And he took bread, gave thanks and broke it, and gave it to them, saying, "This is my body given for you; do this in remembrance of me."
And St. John records Jesus' words here :
But I tell you the truth: It is for your good that I am going away. Unless I go away, the Counselor will not come to you; but if I go, I will send him to you.
13. Brothers, we do not want you to be ignorant about those who fall asleep, or to grieve like the rest of men, who have no hope.
14. We believe that Jesus died and rose again and so we believe that God will bring with Jesus those who have fallen asleep in him.
15. According to the Lord's own word, we tell you that we who are still alive, who are left till the coming of the Lord, will certainly not precede those who have fallen asleep.
16. For the Lord himself will come down from heaven, with a loud command, with the voice of the archangel and with the trumpet call of God, and the dead in Christ will rise first.
17. After that, we who are still alive and are left will be caught up together with them in the clouds to meet the Lord in the air. And so we will be with the Lord forever.
18. Therefore encourage each other with these words.