Could general anesthesia affect the brain negatively ?

Not sure: There is some evidence that with the extremes of age there is some negative effect of anesthesia in the brain. In the pediatric population it is not well understood. In the older population the brain is much more sensitive to both medications and changes or decreases in blood flow. Either of these could have an effect. In our age this is not usually a concern.

Not in adults.: There is no evidence that general anesthesia affects the brain negatively, except perhaps in the extremes of ages. In new born animals (not in humans) anesthesia has been shown to interfere with normal brain development, and in elderly patients it increases the risk of postoperative delirium and cognitive deficits.

May be: There is some interesting, excellent studies about the danger of anesthesia in children less than 3 y/o. Reference: pediatrics volume 130, number3, september 2012. An excellent reading about the subject. Consult a pediatric anesthesiologist for further discussion.