Hi,
It's almost impossible to do properly with 3xAA. You need to tell this to your client.
Their internal resistance is just too high. In addition, voltage is on the low side - if you design to a 1V/cell cutoff, so 3.0V for 3 cells, no voltage sag margin is available at all. If you have to do it with AA cells, you'd be better off with 4xAA and a buck converter capable of 100% duty cycle for low dropout (or a very low-drop-out LDO with 2A current rating). Still, it's very marginal and crappy.
For 3xAA, practically you'd have to buy the best cells available, keep them warm, would only be able to use about 50% of their energy max, and still need quite massive capacitance.
The datasheet excerpt you posted shows
2A for 577us, so given your formula, 3800uF is required. Note that extra drop comes from the ESR of the capacitors. Assuming 100mOhm for the 3800uF elcap, extra 0.2V sag is created at 2A, so you only have dV=100mV left in your formula - recalculate for capacitance, and you suddenly need 11500uF. Now such a massive cap has much less ESR, which again gives you more dV to play with, so if you iterate the formula once more, you are likely to hit somewhere between 5000uF and 10000uF needed. Note that the ESR of the elcap goes up in low temperature, so you need to oversize the capacitors.
For an AA cell, the internal resistance is somewhere around 200mOhm for a FRESH battery, at room temp (
http://data.energizer.com/pdfs/batteryir.pdf ). For a partially used battery, at colder weather, it's
much worse. Even assuming 200mOhm, 3 in series would total 600mOhm, which sags by 1.2V under the 2A load. So it's basically completely up to the capacitors alone to supply the peaks.
Now if you look at the price and size of 10000uF, 6.3V, you'll see why they use batteries to do this instead. And, at the same time, you'll see why all the modern LTE gadgets and phones have relatively large li-ion batteries in them - it's not just to play Angry Birds.
If it has to be with disposable, single use primary Alkaline cells, consider using the large D cells, and 4 in series to give headroom for voltage sagging. It's gonna suck in size and weight, and expense of use.