Thanks for the heads up on this thread :-)
That specific functionality is not built into s2Member. However, you could certainly accomplish such a thing by simply providing a member with a link that leads to the page where your s2Member® File Download link is displayed. s2Member® generates the URL for you; so you can do whatever you like with that URL. If you would like to push it to browser for an automatic download; you might do something like this.
<script type="text/javascript">
setTimeout(function(){
location.href = '[s2File download="example-file.zip" /]';
}, 5000);
</script>
See also: Dashboard -› s2Member® -› Download Options -› Shortcode Attributes & API Functions
See also: http://www.w3schools.com/jsref/met_win_settimeout.asp