A hypothetical emergency situation
The person cannot survive for long, in spite of the infinite supply of blood. 

In real life

There is no blood delivery system that can add blood to the vascular system as fast as it would be lost by two bullet holes in the heart. But I guess that's covered by your conditions. 

As mentioned in comments, where would the blood go? Despite a thoracic entry and exit wound, blood volume inside the thorax would not squirt out of those holes fast enough to prevent a life-threatening accumulation of blood which would interfere with expansion of the lungs, so unoxygenated blood = death. 

Theoretical

I suspect this is what your teacher was hoping would be the answer. Blood - like most things - will follow the path of least resistance. Which has a higher resistance, the aorta and arteries  (if it hit both the right and left ventricles, the pulmonary vasculature as well) supplying life-sustaining blood to vital organs, or two holes? Theoretically, there would be little resistance against blood flow through the holes, so no flow into vasculature means death. 

Regarding clotting, nope. Rate of blood flow would preclude a functional clot. 

In real life, even with surgeons at the ready, this is a deadly scenario. One hole: doable (depending on the caliber of the bullet); plenty of people have survived this event. Two holes, it would take particular circumstances and would basically be a miracle.