The first research I did on this scene related to stopping the heart (the wires were placed directly on his chest). Even though the movie referenced stopping his heart, I determined that his heart would still have to have a trace of electrical activity in order for this to be possible. This is because the stoppage of all electricity in the heart is called asystole, which is also known as flatline. This is considered irreversible and is the signal often used to determine the end of someone's life in a hospital. So, first of all, is it possible to shock the heart with the amount of electricity used in the scene and not die from it. This all depends on the condition of the person's skin.
It takes approximately 12,000 volts to kill a person with healthy, dry skin. However, wet or damaged skin can have upwards of 100 times less resistance to electricity than when it's dry. This means that someone who is wet has a possibility of dying from around 120 volts. Knowing that Hunt used two matching cords from a breaker, it is reasonably safe to assume that they are the building's two hot wires, for which the standard is 120 volts each, 240 volts total. As can be seen in the thumbnail for the video above (refresh the page if the video has already been clicked on), Hunt is particularly sweaty and likely had some damaged skin from his previous fighting. Based on that, it is safe to assume that it would take less than 12,000 volts to seriously injure him. However, he doesn't appear wet enough for 240 volts to kill him, although this is just an assumption. All in all, it seems reasonably possible that 240 volts to the heart could put him into ventricular fibrillation. Vfib is the most serious form of arrhythmia which prevents the heart from pumping blood. It will put the person into cardiac arrest but it is treatable with CPR.
Now that we know the shock and recovery can happen with the right conditions, we must determine whether the shock is enough to disable a charge in Hunt's brain. This was fairly simple to determine with a reasonable assumption. I decided to research a device that is more well-known than a charge implanted in the brain: an iPhone. An iPhone wall adapter takes an input of between 100 and 240 volts and outputs a steady flow of 5-10 volts to the phone. Knowing that iPhone adapters max out at 10 volts, it is not at all a wild assumption that 240 volts would fry a phone, let alone a charge small enough to be planted into a brain. Therefore, I believe that this part of the scene is possible as well.
The final aspect of the scene that I took a look at was the path electricity takes through the body. Hunt held the wires up to his chest, so it was clear that the shock would reach the heart, however, would it also reach the brain. This was interesting because electricity takes paths throughout the body; it does not spread itself out. A shock that enters through an arm will generally pass through the heart and exit out of the other arm. This is the same reason that the recommended stance for surviving lightning is a squat type position with only feet on the ground. Lighting that enters through the legs rarely hits vital organs. However, the best information I was able to get on a path that hits both the heart and brain was a lack of information. I found no such information, which brought me to the assumption that it rarely happened. Therefore, this part of the scene seems the least likely and is the only reason I consider it impossible. However, should I find that a shock can travel from the heart to the brain, my opinion on this scene would change.