An AA is 1.5V (rechargeable AAs are 1.2V).
Once that is established, it all comes down to the mAh.
Most AAs sold these days are listed as 2500mAh, multiply that with 1.5V and you get 3.750 Watts.
Note that this is very close to what you get from a 1000mAh li-ion battery found in many phones (3.7*1000=3700).
Now with a external li-ion emergency battery you will get conversion losses, as it has to go up to 5V for the USB and then back down again at the other end.
Considering that different phones consume different amounts of energy, and that different AA batteries have different capacities, that's hard to say.
If you carry a Wiko Lubi like me, you can probably talk more than 10h with a single battery. If you carry an energy-hungry smartphone, you'll probably get an order of magnitude less.