Curtis,
Your assumptions are right on target. But, I would grind on the edges just a bit.
If a device is rated at 8 Amps, it is very likely to actually draw a bit less, or almost all units produced would draw less (normal manufacturing variation). When dealing with one device it is realistic to just go with the stated rating, but when looking at more than one device it is reasonable to assume the pair would require a bit less than twice the actual rating (it is very unlikely that you would end up with two units that both draw the 8 Amp maximum current).
So, it is very reasonable to think that two Alien Bee units rated at 8 Amps total would very likely work just fine on 15 Amp circuits common in households in the US, so the also very common 20 Amp circuits are likely to be more than adequate. It is also very likely (repeat likely) that a 20 Amp circuit would accommodate three of the Alien Bee units rated at 8 Amps each.
If you were using more than one power pack, on systems with a power pack and flash heads, they would work exactly the same way. But, the number of flash heads plugged into the power pack system would not affect the Amp requirements. Power pack/head systems either give all the power to one head, or divide the same amount of power with several heads. They are not like incandescent bulbs where increasing the number of bulbs increases the amount of light output.
Some larger capacity flash gear (like many Speedotron Blackline 1200, 2400, and 4800 W-s units) that tax some power circuits, actually have switches to slow down the recycling (limits maximum current) so they can adapt to marginal AC power. You recycle slower, but you do not trip circuit breakers or blow fuses. In most cases the slower recycling is not required, but in some old electrical service situations, the slower recycling is necessary.
I find it nice to think of the power capacitors in these units as buckets, and the power supply components as water pumps. All of the Alien Bee flash units seem to share the same pump. The B1600 has four buckets (power capacitors), the B800 has two buckets, and the B400 one bucket. It just takes longer for a pump with a fixed pumping capacity to fill four buckets than one. But, the maximum amount it can pump is very like the Amp rating, so it is the same for the B400, B800, and B1600.
I suspect there will be some on the forum that will predictably assume the bottom line of always being intrinsically safe and never using two 8 Amp devices like this on a 15 Amp circuit, but I also know you are a a pragmatic human where reasonableness transcends anal fastidiousness.
As a trivial aside, and just as an annoyance, you seem to be giving James Watt is due (W), but slight André-Marie Ampère (a).
Enjoy! Lon