Can bleeding during a pap smear cause abnormal results?

Yes. Yes, pap smears ideally are collected when menstruation is not occuring.
Obscure. Collecting an abundance of blood during a pap smear will not "cause" an abnormal result, but as was mentioned, can obscure the interpretation of the pap smear. There are several maneuvers that the pathology lab can do to mitigate the obscuring blood.
Rarely. We never say never, but doing a pap smear during menses may result in an unsatisfactory smear in that the blood is covering the epithelial cells so that the pathologist simply cannot "read" the smear. But if the amount of blood is small, frequently the pathologist can still accurately interpret the smear.