If your placenta is completely covering your cervix, can it cause period like cramps & spotting?

Absolutely. What you describe is called placentia previa. It often causes painless vaginal spotting but can also cause crampy pain. With this condition, the placenta can separate from the uterus as the cervix dilates at term, leading to significant bleeding at delivery and risk to the mother and child. An ultasound is needed prior to delivery to determine placental location and risk for mother and baby.