As Miracle Max would say, there's two kinds of dead batteries, and there's a big difference between them.
This is the most common kind of dead battery. Let's say your battery is rated for 300 cold cranking amps. After several years of use, it degrades until it reaches, say, 250 amps. Your battery isn't out of power, it just can't get your engine over the hump of cranking amps. Incidentally, in this scenario, "letting the battery charge" won't help because the battery is no longer capable of holding sufficient charge.
Jumping in this scenario works by borrowing the remaining amps from an external source. This is why even a small car can often jump a large pickup. You can even buy battery chargers that can plug into a wall and will give you that boost as well (both batteries and wall chargers do this via a capacitor). These smaller jumping batteries are designed to give you surge in cranking amps for a single moment to give you that extra push. Depending on the device, that could be as little as 100 amps or as many as 2000.
After you've gone through the battery's pockets for loose change... wait, we're talking batteries. Sorry, Max.
An "all dead" battery is really a good battery that is mostly or fully depleted (i.e. you ran your car radio with the engine off for a long time or your alternator died). This is a less common problem, but it still happens. A pure surge battery isn't designed help you directly with this problem because it's generally designed to offer a one-time boost. Your lead-acid car battery really wouldn't like getting 500 amps all at once.
Lead acid batteries like a slow, steady charge. Most wall-powered chargers run 15-30A in charging mode and you'll need to charge it for some time (meaning several hours) to get it back up to full.
If I were to have been jumping the dead car with another car, I would have given the dead car's battery a good long charge from the donor car before trying to start it.
The reason people are taught to "let the car charge a bit" first in jumping is that you need the dead battery to provide some power in the attempt to crank. Since you're probably not carrying a battery tester with you, there's no way to know why the battery is bad, and there's no harm in letting a "mostly dead" battery charge for a minute.
If you're using a battery pack, just hook and crank. If the battery is all dead, the alternator will recharge it naturally. If the battery is mostly dead, it will provide the missing amps. Go take it to a car parts place and they can test it for free and tell you if you need a new battery.