When birds hit our windows, and if they're on the ground, I keep watch (inside) to make sure no predators can get to them before they can recover and take off. During the winter months, when it's cold, if they don't fly off immediately, I will sit outside and hold them in my cupped hands (for warmth) in the sun and in the lee of the wind until they can hop or fly out of my hands. This has sometimes taken anywhere from 15 minutes to nearly an hour when the temps are low, but I haven't yet had one die in my hands. I've had several, however, that have died almost instantly from, I assume, a broken neck or other internal trauma.
Don't know about the heart attack response, but birds are very sensitive to stress and handling them certainly adds greatly to it if not done very carefully.
The only hummer that hit one of our windows landed on the deck and lay stunned. I did not pick him up -- they're extremely fragile -- but instead moved a couple of flower pots around to give him a little more cover, and in less than 10 minutes he buzzed off.