As Archer explained the power reserve is the same, as the mainspring will take the exact same time to unwind.
What changes is the minimum power needed to move the hands, because, with the chronograph on, you now have more weight to move and friction to overcome each time the escapement opens. And the watch will stop, not when the power reserve is exhausted, but when it is below the new, higher, minimum needed to move the movement and the hands.
In fact, if you then disengage the chronograph, the watch will probably start running again for a while, showing clearly that the power reserve was not exhausted. It was just too low for the increased load you were putting on it, but ok for a lighter load.