Thank you, Joe, for the quiestions:

<H1>What window manager are you using?</H1>

I tested it on two systems
<H2>Thin Client with Ubuntu and Openbox and TCL 8.6.0</H2>
<H2>Virtual PC with CentOS and Gnome and TCL 8.5.7 and 8.6.1</H2>
When I click "About" in the gnome desktop, it returns:
  *   CentOS 6.5
  *   Kernel 2.6.32
  *   Gnome 2.28.2
CentOS is often quite old. TCL is at 8.5.7 (why I also tested on 8.5.7).
TCL/Tk 8.6.1 is compiled by me.

<H1>After [wm state . iconic], does the window actually reappear iconified (in the task bar, usually), or does the WM leave it withdrawn?</H1>

The window appears iconified.

The issue is that "wm state ." returns "withdrawn" but it should return "iconified".