Will visible veins disappear after I have the baby?

Probably some. These should get better but may not completely disappear. The best way to manage these is to prevent them by wearing support hose during the pregnancy. Tell your friends!
Not completely. Any varicose veins that you develop during pregnancy will decrease in size and become much less noticeable, but they won't go away completely, as dr. Gorski said. Wearing support stockings during pregnancy will help to control symptoms from these veins, while you wear them, but there is no data to make us think that support will prevent varicose veins from developing during pregnancy.