Can I run an Arduino off 8 x AA batteries?
The first thing the power jack goes to inside the Arduino is a 5V regulator.

This can (for the UNO at any rate) supply a maximum of 800mA.

Any more than that and you will have to use the external power.

How much current the AA batteries can supply depends on the chemistry.

But yes, you can run (and many people do) off 8 AA batteries.