Can propranolol make birth control not work well?

No. Propranolol does not affect the effectiveness of birth control pills. However, bcp can on rare occasions elevate blood pressure. You should periodically check your blood pressure while on bcp's.
Probably not. Combined oral contraceptives (most birth control pills) may increase the potency of propranolol, so it is important for your doctor to be aware of any birth control methods you may be using. There does not seem to be any effect of Propranolol decreasing the efficacy of any birth control method. Let your doctor know if you get pregnant while taking Propranolol as there are risks to the fetus.