Unfortunately, no.
While two successes isn't terrible, keeping a man alive after a gun shot wound isn't a simple task. Elizabeth does her job, going through the full routine, keeping her beast in check despite all the blood pooling around her. Luckily she wasn't hungry, or she may have given in.
The man is still alive when they get to the hospital, but it's obvious that he's not going to be long. The shot resulted in blood in the lungs, and you simply did not get to him in time. While you managed to get him breathing again, the brain damage from lack of oxygen had already started, and the machines in the bus were the only thing keeping him alive. Of course, the doctors do their best, but by the time all the shrapnel from the bullet is found, it's too late. He dies on the operating table.
A review happens, as it always does when someone dies. But, Elizabeth did her job well. Kept calm, and really pushed to keep him from slipping away. It wasn't enough to save the man, but it was enough to keep her out of a drug test, and the physical that comes with it.