I am going to answer this question directly; yes, a child conceived in rape DOES have every right to live. Don't get me wrong, I am not saying that as a woman, I would want to become pregnant because someone raped me - regardless of what kind of rape it was. Furthermore, a woman who conceives a child in rape WOULD inevitably never be fond of remembering the circumstances surrounding the pregnancy of the child, but none of that makes an abortion justifiable at all and I am able to explain why using several reasons.
Firstly, yes it does take sex to bring another person into the world, but no person who has ever been conceived simply because of a sexual act. All people are three- fold beings having a body, spirit and also a soul. Two parts of that three fold being cannot be attributed to the physiological functions of any person, the soul and spirit. The sexual act brings forth the physical body, but that's as far as it goes. Therefore a woman can only conceive if God decides it's okay for someone made in his image to come into the world through her. Secondly, it still would take DNA from her for her to conceive that child. As for a child being a constant reminder, he/she would be in a sense because the woman knows that the child didn't come into the world through her as an attribution to sex she wanted, she was raped. Be that as it may, rape victims who don't conceive as a result don't forget the attack/violating encounter all just because they don't have a "constant reminder" in the form of a child from the rape.
No child should be denied the right to exist, or for that be loved or shown affection because of not being conceived under ideal circumstances. Many women who have conceived in rape resent the resulting children because often times the child remainds them that the rape happened. If a woman is able to work through those negative feelings she and her child can have a positive relationship. Two wrongs don't make a right. Adoption is an option.