Does a woman need to cover her hair during childbirth or other major medical procedures?
not likely. would be similar to asking would a women need to cover her hair when showering. when one is in the midst of something which requires to be disrobed then at that moment we aren't concerned with her not being covered. if someone was normally covered in blood they wouldn't pray nor say G-d's name yet when the cohanim were in the middle of offering the avodah we weren't concerned with them being dirty while they were in the middle of it. context is an important factor when making decisions. a funny when to put it... knowing that tomato is a fruit is knowing a fact but wisdom is knowing that you don't get a smoothie if you put it in the blender