There isn't a predefined way, but you could override the Message.File() method and cause the file messages to have a visibility time of 0 (so they will be removed immediately). Here's an example:
<!DOCTYPE html>
<html>
<head>
<title>Hide Loading Messages</title>
<script type="text/x-mathjax-config">
MathJax.Message.File = function (file) {
var root = MathJax.Ajax.config.root;
if (file.substr(0,root.length) === root) {file = "[MathJax]"+file.substr(root.length)}
return this.Set("Loading "+file,null,0);
}
</script>
</head>
<body>
\[x+1\over x-1\]
</body>
</html>
This still means that the messages will be saved in the log, but they won't show up on the screen.
Hope that does the trick.
Davide