Innocandy asked me on my Help-Site forums about doing this, so I'm adding the code here as well.

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Hiding the Shout Box from Non-Members

This script reveals a hidden shout box. So what that means is anyone can view the page source and still see the shout box contents... if you want to completely remove the shout box, then that will take another bit of coding (included at the end).

Coding
To start out, you will need to hide te shout box. The CSS at the top of the code does that. while the script will reveal the code if it doesn't find a link to join the site. Add the complete code below to your Footer Area (Control Panel > Custom HTML & Script > Footer Area).

<!-- *** Reveal shout box if the link to join the site doesn't exist *** -->
<style type="text/css">
 .gpWidget-shout { display: none; }
</style>
<script type="text/javascript">
$(document).ready(function(){
 var accessLevel = "$block[userlevelname]";
 if (!accessLevel.match('public|associate')) $('.gpWidget-shout').show();
})
</script>

If you want to completely remove the shoutbox (personal preference I guess), then add this code:

<!-- *** Reveal shout box if the link to join the site doesn't exist, otherwise remove it *** -->
<style type="text/css">
 .gpWidget-shout { display: none; }
</style>
<script type="text/javascript">
$(document).ready(function(){
 var accessLevel = "$block[userlevelname]";
 if (accessLevel.match('public|associate')) {
  $('.gpWidget-shout').remove();
 } else {
  $('.gpWidget-shout').show();
 }
})
</script>

Customizing

• Modify the access level by changing the code in blue. Any additional access level names should be separated with a pipe "|" (shift-\, above the enter key on the keyboard). Here are some examples:
  
  

  Access Levels		Hide Shout box from	Code
  Public   Associate   Member   Council   Officer   Super Admin		Public	'public'
  		Public & Associates	'public|associate'
  		Public, Associates & Members	'public|associate|member'



• The code is using a new variable "$block[userlevelname]" which provides the access level name in lower case.

Edit (1/22/2010): Updated the code to look for "membership is pending review" in the top menu and if found, it won't show the shout box. NOTE: this feature doesn't work if you are using a Navigation type of "Content Box - Left Side, Center or Right Side".
Edit (1/31/2010): Updated to use the new $block code that provides the user access level.