Is there a JavaScript alert that doesn’t pause the script?

You could do the alert in a setTimeout (which a very short timeout) as setTimeout is asynchronous:

setTimeout("alert('hello world');", 1);

Or to do it properly you really show use a method rather than a string into your setTimeout:

setTimeout(function() { alert('hello world'); }, 1);

Otherwise you open yourself up to JavaScript injection attacks. When you pass a string it is run through the JavaScript eval function.