Well a mixture of both, but it depends on the A/D conversion method the chip uses.
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Flash conversion - mainly instantaneous
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Successive approximation - as the sample is evaluated from the most significant bit to the least then it will depend when the disturbance occurs as to how messed up are the smaller bits.
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Dual ramp - during the integration phase yes it will average, during the discharge phase it will not matter if the input changes at all.