you can still position the icon somewhere at the bottom of your website.
If this doesn't help, you can still try to edit your template and wrap the
<?php mosLoadModules('nameOfModule'); ?>
<div style='display: none;'>
<? mosLoadModules('nameOfModule') ; ?>
Regarding the second question: no, there's no reason would like joomlawatch users to overload my domain with various requests from around the world
You can examine the PHP code if you want.
Hope it helped,