Yes it's possible to scare a rabbit to death and I did the exact thing as a kid to a rabbit I really loved.
I was not trying to kill the rabbit but I was just a 7 year old kid and was out playing and decided to just try to sneak up on the rabbit and scare him for fun even though I loved that rabbit.
The rabbit died after I scared him really bad because the scared rabbit got a heart attack from me scaring him.
The rabbit didn't actually die from just being scared but because when I scared him he got a heart attack which killed him.
Some other things that can give a rabbit or rabbits heart attacks are Loud sounds, such as cats, dogs, loud music, or screaming.