It depends on the type of anesthesia. If she is given a neural block, that is not supposed to affect the baby.
A neural block, or spinal block, is often used in Caesarian section, so as not to affect the baby.
Substances that are inhaled, or given intravenously, can be expected to be also transmitted to the child.
I was just going by what the surgeon said; he did not say what type of anaesthesia, just that both mother and child were under the effects.
That is an interesting fact...