Despite the publication of simplistic hit pieces specifically created to counter "fetal-pain" legislation, the answer is "Yes":
Currently there are several centers in the U.S. doing surgery on second and third trimester fetuses, typically using general anesthesia for both mother and the unborn child for the more invasive procedures. It is clear from a study of fetal surgery that the unborn benefit from sedation and anesthesia. Vivette Glover, a researcher at the Queen Charlottes and Chelsea Hospital in London has stated that not only third trimester fetuses should have pain relief, but also thatRead the rest by Mary L. Davenport at the American Thinker.
...between 17 and 26 [weeks] it is increasingly possible that it starts to feel something and that abortions done in that period ought to use anaesthesia
HT: Thomas

