AA Alkaline batteries may be assumed to have a capacity somewhat in excess of 2000 mAh. This varies with load but at C/2 rate (see below) they will have most of that. [ Carbon-inc - inc Chloride or 'Le Clanche' have less capacity and ability to suppo high discharge and will do poorly here]
USB spec is ~ 5V and you are charging LiIon that reach 4.2V at full charge.
Alkaline cells start at almost 1.6V, rapidly drop under 1.5V and the discharge at very very approximately linearly decreasing voltage down to say 1V.
At 1.6 x 4 = 6.4 V some badly designed devices that do meet USB spec MAY be damaged. Not usual.
At 1.25V x 4 = 5V you drop under nominal USB spec voltage, and allowance for voltage drop in pack wiring and connectors takes you lower quicker. Charging at a possibly reducing rate will continue down to say 4.7V - maybe lower.
4.7/4 = say 1.2V/cell.
So available range is (1.5-1.2)/(1.5-1.0) = 0.6 = say about 60% of capacity - maybe more.
So you may get 60% x 2000 mAh+ = 1200 - 1500 mAh out of a pack of AA Alkalines.
Many cellphones have battery capacities under 1200 mAh and LiIon current charging efficiency is excellent (as opposed to energy efficincy which is good but lower) so you'll fully charge many cvellphones.
LiIon with as much energy available as desired charge at typically 1C for about40 minutes and then tail off at reducing current for 2 to 3 hours total. Total time also affected by current cutoff decisions. As peak current into a say 1000 mAh cell will be 1000 mA this is about C/2 for Alkaline cells so while capacity will be down it will not be terrible compared with nominal capacity.
NimH - will be less satisfactory. Vout ~= 1.3V oc when fully chaarged. Drops into 1.1V to 1.2V across most of range depending on discharge rate. At C/2 it should be closer to 1.2V for a lot of the ime. This gives 4 x 1.2 = 4.8V before resistance drops. Under USB spec and very marginal. May work in selected cases but no guarantee in any one case.
Connector: will be able to be done cheaply despite non-standardness. Chinese can and do implement almost anything they wish that will "almost work well enough most of the time" at a throwaway price if they want to. (I have reasonably extensive first hand Chinese factory experience of the general willingness to do anything if they want to - and not to do so if they choose not to).