Not at all

The webcontainer needs an id, example:

<h2 id="webpart-header">Headline</h2>

Then I have a small javascript function that is attached in an external js file:

/* Hide Webcontainer via javascript if empty*/
function hideLayer(element) {
elem = document.getElementById( element );
elem.style.display = "none";
}

****
Now in the wep part configuration, at no data behaviour, you uncheck the checkbox and call the js function by entering following script in the no record found text:
<script type="text/javascript">hideLayer("webpart-header");</script>

Whereby webpart-header the id name of your container is. You could also have a more complex <div> structure here.

And you are done.

ralph