>If the activate code is moved to macosxSupport.activate(), does the
>following work in EditorWindow.open_turtle_demo?
>cmd = [sys.executable, '-c',
  'from idlelib.macosxSupport import activate as A; A()\n'
  'from turtledemo.__main__ import main; main()']
>Does the activate code have to be called after, say, the tkinter import in
>turtledemo, or is anytime in the process ok?

The activate code has to be called in the subprocess after Tk() has been called because only then is the subprocess guaranteed to have been promoted to an OS X GUI process.  So that suggestion will not work.  The idea of adding something to tkinter was discussed in msg192523 of issue11571, though not this specific solution.  If you want to pursue more generalized issues of GUI application behaviors on OS X, that should be the subject of another issue.  I suggest that this issue remain focused on the original topic.  I also would be concerned about adding the Run menu to the Shell window (or system menu bar when the Shell window is active) merely to accommodate this feature.  Having turtledemo in the Help menu seems fine to me.