I know I'm late to this party, but the question about the behavior of power-on reset ICs is a common one.
>> Usually these sorts of chips spell out clearly how they react to a full power cycle but this one just... doesn't.
Actually, it does; the answer is in the Electrical Characteristics: The minimum operating voltage is 1.0 V. When Vcc is below this minimum, the output drive is undefined. For an open-drain output device, the output will simply float to whatever voltage is being applied to it externally, e.g., through a pullup from Vcc.
A common way to generate a POR signal that is valid all the way down to zero Vcc is to choose an active-low reset, totem-pole output device and add a pulldown resistor to guarantee a low output below the device minimum Vcc. Although the data sheet does not guarantee that the device won't inadvertently source current to the output when Vcc is below the minimum, I've never known that to happen in practice.
Regards -- CW