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To what degree are the power requirements on their faq still valid for the pi zero ? https://www.raspberrypi.org/help/faqs/#power

The question I really want to ask is, how long will a 1.2A supply last with nothing else attached to it ?

Your question isn't meaningful, because amps are a measure of the rate at which a power supply can provide current.

An AA battery can provide 1.2A for maybe an hour or two; a wall wart can provide 1.2A indefinitely.

He most probably meant 1.2Ah

Reportedly draws ~80 mA idle and ~160 mA [1] (I assume with no peripherals whatsoever). So a 1.2Ah battery should last between ~7-14 hours.