If scripting is enabled, the noscript element is defined as containing only text - though it must be parsable text, with some restrictions on content. With that in mind, you should be able to extract the text, parse it, and then find your desired element. A rudimentary example of this follows:
var nos = document.getElementsByTagName("noscript")[0];
// in some browsers, contents of noscript hang around in one form or another
var nosHtml = nos.textContent||nos.innerHTML;
if ( nosHtml )
{
var temp = document.createElement("div");
temp.innerHTML = nosHtml;
// lazy man's query library: add it, find it, remove it
document.body.appendChild(temp);
var ex = document.getElementById("example");
document.body.removeChild(temp);
alert(ex.innerHTML);
}
Note that when I originally wrote this answer, the above failed in Google Chrome; access to noscript content appears to be somewhat better-supported these days, but it still strikes me as an edge-case that is perhaps somewhat more likely than other elements to exhibit bugs - I would avoid it if you've other options.