I don't think there is any way.

If you have comment balloons turned on (Tools > Options > Track Changes tab),
the Reviewing Pane seems to open automatically only if you are in Normal view
or Outline view. If balloons are not turned on, the Reviewing Pane seems to
open in any view.

The command executed by Insert > Comments is named "InsertAnnotation". You
could save the macro below, e.g. in your Normal.dot, and it will run instead
of the built-in command. The macro inserts a comment. If this causes an extra
pane to be opened, that pane is closed by the macro (see the notes below).

Sub InsertAnnotation()
   Dim n As Long
   n = ActiveWindow.Panes.Count
   'Add comment
   Selection.Comments.Add Range:=Selection.Range
   'Close the Reviewing Pane or the Comments Pane
   'if it was opened
   With ActiveWindow
       'If a new pane was opened, close it
       If .Panes.Count = n + 1 Then
           .Panes(n + 1).Close
       End If
   End With
End Sub

----------------
Notes:
With the macro installed, I have observed the following:
If comment balloons is turned _on_: When the comment is inserted, the
Reviewing Pane opens if you are in Normal view or Outline view (this was
expected) - the pane is closed again by the macro. But was also happens, is
that the _Comments Pane_ for some reason is opened if you are in any other
view when inserting the comment (I cannot explain why) - that pane is closed
again by the macro.

If comment balloons is turned _off:_ The Reviewing Pane opens in any view
and is closed again by the macro.

In case of e.g. the footnote/endnote pane, it would be possible use the
following line of code to check whether the selection is in that pane:

Selection.Information(wdInFootnoteEndnotePane)

For some reason, a corresponding constant "wdInReviewingPane", does not
exist. However, "wdInCommentPane" exists.

That is why the macro is created so that it just checks whether an extra
pane was opened and, if that is the case, closes that pane again.