No, they cannot become a "real person" in the sense that they will have a real body, standing in front of you and able to be seen and interact with the real world like any other human. However, they can have a real mind, with their own thoughts and feelings unique from yours. Some tulpamancers can also train themselves to hallucinate their tulpa, so that you can experience them with your own senses, but they won't be any more physically real than say, a dream in that scenario. Just something that your mind tricks you into perceiving when its not really there. So, the flat answer is no, but they can seem real in many ways with enough practice. And no other person will ever really be able to see them besides you, either. They cannot be seen by any other person no more so than another person can see their thoughts. One would have to be able to read your thoughts (as in, telepathy) to experience your tulpa firstand.
tl;dr: It's pretty much impossible as far as science is concerned