Can MDI child be minimized to an ICON?

Yes it's possible and no, it's not easy.
If you use Windows NT 3.51, it's easy enough, just don't do anything.(About win 3.51 look)
It's because the implementaion has changed in  NT 4 and Win 95 that this behaveour has changed.
First you have to remove the bar:
That's easy enough here's an example

procedure TForm2.FormResize(Sender: TObject);
begin
  //Mdi child close *without* titlebar
  if windowstate=wsMinimized then
  if ShowWindow(Self.Handle, SW_HIDE)=true then
   //in Real life you would create this dynamically,
and add code to do an 'Arrange Icon'
  form1.image1.picture.Assign(self.icon);
end;

The doubleclickhandler for the Image should read:
{You can lookup the MDIchild in ther MdiChildren list}
procedure TForm1.Image1DblClick(Sender: TObject);
begin
//This is for one mdichild only, but you can expand the imagelist
//With a property 'AssociatedChild' or something
      SetWindowPos(form2.Handle, HWND_TOP, 0, 0, 0, 0, SWP_NOMOVE OR
         SWP_NOSIZE OR SWP_SHOWWINDOW);
       Windows.SetFocus(Form2.Handle);
end;

Although by no means complete, that's a way to do it.