Can chemotherapy harm your baby if you're pregnant?

Complicated. Surprisingly, there are many chemotherapies that are well tolerated in pregnancy, for both mother and baby. That said, its a serious issue that has to be handled on a case by case basis with a high risk OB and an oncologist.
Could be. It is a very complicated situation. It will depend on the type of cancer, how urgent the chemo needs to be given, type of chemotherapy and how far the pregnancy is (which trimester). Chemotherapy, as much as possible- has to be avoided on the first trimester. Some chemo can be given on the second or third trimester. You should discuss this with your oncologist and high risk pregnancy doctor.