Yes, I do believe that offspring have a right to know their biological parents, but I don't think that knowing would actually lead to a higher rate of abortion. I think if the child is interested in finding out who their biological parents they should have the right to do so.
As long as the genetic parents are willing, a child has a right to know where they came from. It helps a person psychologically to understand where they come from. It also helps to know the medical background for the health of future generations. Knowing this will not lead to a higher rate of abortions. If anything, having knowledge of this information will help prepare a better future for the upcoming generations.