pardon the ignorance, but my assumption is that the rating of the transformer will determine the rate at which the batteries recharge - not which headphones the o2 can and cannot drive. but I imagine that if listening while recharging, an insufficient psu could result in a slow battery drain. if an insufficient transformer just means that it takes a little longer to recharge, then the concern is less of a concern, but if the batteries/circuitry could be damaged over time, then there is a concern.
I'm using the o2 with 32 & 300 ohm cans.
Check the circuit (click for legible size, please excuse the quality):
Each battery is charged by the output of the respective regulator (7812 for positive and 7912 for negative), through a diode and the 220 ohms resistor. The regulator output would have to be really really low (+12V regulator outputting less than the battery voltage, almost, i.e. waaaaaay out of regulation), for the battery to actually be powering the amp.
Rate of charging just depends on the regulator output (should be about +12V, -12V) and current battery level. It pretty much just charges as according to what you see in the circuit and Ohm's Law: (Regulator output voltage - diode drop voltage - current battery voltage) / 220 ohms is the trickle charging current. That's not related to the AC adapter rating, except unless it's far below the point where the regulator output voltage is significantly affected.
As for the voltage the regulators receive (needs to be a certain point like 2V above +12V or so, or however much the drop is), that depends on the AC line voltage, transformer, how much the capacitor discharges between cycles on the AC input. Capacitor discharge between cycles depends on current drawn by the amp, thus the discussion about how much power is being used, which in turn depends on what headphones you're using and how loud you're listening and whether or not you're charging the battery, etc.