Really depends on how fast you catch the cardiac arrest. If it is a witnessed arrest, there is a reasonable chance that HIGH QUALITY CPR (mainly chest compressions) can keep the person from being permanently dead. Most lay-persons do not do chest compressions hard enough and fast enough. Of course being able to restart the heart depends on the original cause(s) of arrest. In my educated opinion/experience listed in order of most likely to reverse to least likely (WITH hospital care at some point):
HYPOXIA (low oxygen, probably the easiest to fix: drowning, compromised airway, allergies; in the hospital I've seen a lot of people come back from this);
HYPOVOLEMIA (bleed out, you didn't put that tourniquet on fast enough or effectively; kinda screwed unless you have IV access and fluids/blood, easy to fix in hospital, nightmare to fix outside);
TOXINS (wide range of possibilities; poisonous snakes, insects, etc. Needs toxin specific medication/care),
MI (myocardial infarction/heart attack; this is where the AED comes in, though you might get shockable rhythms at any point during CPR regardless of the cause);
SEPSIS (infection, once you get multi-organ involvement the prognosis is very bad).
I'm sure of missed a bunch (hypo/hyperthermia etc.), and this is all assuming the person is already pulseless. The best way to PREVENT cardiac arrest is to treat the underlying conditions early/quickly. This is where training comes in. Learning how and when to open an airway: chin thrust/head tilt, recovery position, nasopharyngeal airways. Putting on a tourniquet quickly (10-20 seconds), or even possibly on your own leg/arm after being shot is not easy even if you practice frequently. Keeping one or more well designed tourniquets on your person/vehicle saves time you may not have to improvise a solution, though in some cases (multiple limbs, multiple casualties) you will run out and need to improvise.
I recently took the Bullets and Bandages I course at Sig and I definitely thought it was worth the money as a medical professional that does NOT often deal with trauma. If you are an EMT/paramedic much of the training would be redundant. For the lay person / recreational shooter it is a lot of material but also worth it. The NES Summit is also having a medical course on the first night.