No, June would have moved herself back upstairs because the shot to her from above wasn't a fatal one.
OK, but wouldn't there be a significant blood trail to indicate this? My understanding (I may be wrong) is that the police did not find blood on the landing or the main staircase itself. The only blood in that general location was on the wallpaper of the main staircase, indicating movement by Nevill.
Another thing that points away from the possibility of June being outside the master bedroom after having been shot is that there is blood under the window of the master bedroom, which indicates she was walking around after having been shot during the first fusillade, yet there isn't much blood anywhere else.
Actually, it would be useful to know: Did the police compile a blood map?