Glad it went okay. Just for future reference, the anesthesiologist is never sterile at the head of the bed, and your head is never sterile unless you are getting head surgery.

The head and usually upper arms and chest of a patient undergoing surgery are left unsterile. A drape is hung separating the abdomen/limbs from the head so that the area being operated on below the drape can be sterilized.

Anesthesiologists don't scrub-in to intubate or do anything at the head of a patient. They just wear regular exam gloves like your family doctor would (eg. to do a rectal exam to check a prostate gland).

If your hairpiece came free in the OR it would be embarrassing and kind of surprising to everyone (which might shock them) but it wouldn't directly contaminate anything no matter how it fell (assuming again it isn't head surgery).

And if it is attached well there's no reason it would fall off. Anesthesiologists don't make a general practice of grabbing onto patients' hair and pulling.