In some cases. My first experience with my wife in an ER (there have been many!), the doc came up to us and said exactly this. They needed to reposition a broken bone so it could be put in a cast before surgery to rebuild the wrist could be scheduled. Since it would only take a few seconds, instead of anesthesia they would use a medication that would let her be aware of the process, but she would forget it almost immediately after.

That was about 20 years ago. To this day, the last thing she remembers is lying on the table and saying "OK, let's git-er-done" and the next 5-10 minutes are missing.