This discussion of Alkalines peaked my curiosity so I did a load test on a brand new Duracell AA battery. I found voltage sags 150mV with a 1A load which is 150mΩ internal DC resistance for the cell. I've measured AA NiMH cells in the past and they are close to 100mΩ.
So, with a nominal open circuit voltage of 1.5V per cell, 3 Alkalines in series would provide 4.5 Volts. A 3Ω atomizer plus the 450mΩ total internal resistance of the cell pack would result in a current of 1.3A. Multiplying current with the internal resistance of the pack results in a voltage sag about 6 tenths of a Volt. That means actual voltage delivered to the atomizer would be 3.9V, probably acceptable.
Lets do the same calculation for 4 Alkaline cells. That would be 6V open circuit, but with the extra cell, internal resistance of the whole pack is 600mΩ. With a 3Ω atomizer, resulting current would be 1.67A. Multiplying that with the internal resistance of the cells yields 1V sag. That results in a voltage at the atomizer of 5V. That's actually a more ideal voltage for vaping.
As a comparison, lets do the calculation for 4 NiMH cells. Open circuit voltage would be 5.2V (open circuit voltage is actually closer to 1.3V for NiMH cells). Cell pack resistance would be 400mΩ. Resulting current with a 3Ω atomizer would be 1.5A. Sag would be 600mV. That would be around 4.6V delivered to the atomizer.
The conclusion is that for an ideal voltage, four Alkalines in series would be preferable to three, but three would work with a voltage of 3.9V at a standard resistance atomizer.
Another consideration is cell longevity. A Duracell AA Alkaline battery has around 3000mAh of charge capacity. That does not add for a series pack so that number applies to either a 3 or 4 cell pack. Using the 1.67A of a 4 cell pack, you'd get 1.8 hours of continuous run time. Using a hit length of 5 seconds that would be about 1300 hits. With an average of one hit per minute, that would be a little over 20 hours of run time or a rate of 150mAh per hour. I'm a heavy vaper and can use as much as 250mAh per hour, but 100mAh per hour is probably a better average. That would be about 2 days of vaping.
Looking at cost, you can find AA Duracell copper tops for as little as $1 a cell. Using four cells that last two days results in a cost of $2 a day. Though, you can get other brands cheaper, but they may have lower charge capacity and higher internal resistance which could be a problem. $2 a day is not unreasonable, but it's certainly much more expensive than using a rechargeable cell. A 4 pack of NiMH AA batteries is around $20 and can last as many as a thousand charge cycles. Li-Ion cells are similarly economical in comparison.