Rephrasing my previous question: On a person with a lung filling up with blood, would an AED or CPR be used?

I probably labeled my previous question wrong--though the answer given was very informative--so I'll rephrase. If a person's lung(s) are filling up with blood, is CPR possible due to that every time you would pump the chest, blood would come from the lips? In the case I'm referring to, the paramedics knew that the person's lung were filling up with blood, because the patient was coughing, and blood was spewing from her mouth. If the woman's heart stopped, would they attempt CPR even though blood would come out her mouth, or would they just use an AED to get the heart pumping again?