Propranolol won't stop your heart at normal doses; it just slows it down, lowers your blood pressure and calms you down - regardless of how you're feeling.
It's perfectly safe, I've used the stuff pretty aggressively over the last year in conjunction with many meds. Only problem I've had is a little bit of high blood pressure after it wears off, but I'm taking 160mg extended release a lot of the time.