1 You can have light bleeding during pregnancy and spotting yes. 2  A normal heavy flow period is very unlikely during pregnancy but it does happen with some women. 3  Yes, but it is not called a period. 4  There is a technical term used for the bleeding during pregnancy. A period is to drain your menstrual blood, lining and eggs, which in pregnancy are needed to protect the fertilized egg or eggs. 2  So there for you CAN NOT be pregnant and have your period. 3  I'll explain why some women THINK they are on their period.