We should distinguish between the usual menstrual cycle bleeding and other types of bleeding. The cycle is related to ovulation and associated hormonal changes. During pregnancy, ovulation does not exist and therefore any bleeding during pregnancy is pathological due to abortion or other causes.
Yes, it''s possible to have spotting bleeding like a period (breakthrough bleeding) at about the time that woman''s period would have been due. The reason is due to non fusion of Decidua parietalis and Decidua capsularis and it is called decidual bleeding.