No, the rate tolerances are all with the chronograph stopped. Rates are not checked with the chronograph running but the balance amplitudes are.
The reserve is a function of mainspring length and gearing, so it is designed into the movement and doesn’t change. However the increase in load from the addition of the chronograph mechanism will mean that a greater torque is required to keep the watch running, so it will stop sooner than it would than if the chronograph was off. But when the watch stops, if you turn the chronograph off the watch will start running again.
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