No, the genetic constitution of mother does not play a significant role in determining the sex of baby. This is because mother has 2 X sex-chromosomes (i.e. XX) so the baby will inherit an X chromosome from the mother. It is the father whose genetic constitution plays important role. Father has XY sex chromosomes so the baby will either inherit X chromosome or Y chromosome through sperm. If the sperm carries X chromosome the baby born will be a girl (XX) and if the sperm carries Y chromosome the baby born will be a boy (XY).