Generally, no chance.
It would be possible under very special circumstances. The page would have to be a hypertext application (.hta) to be able to access the file system at all, and the server would have to be in the same local network as the client.
Here is an example of an .hta page using the FileSystemObject
object to read a file from the server:
<html>
<head>
<title>File</title>
</head>
<body>
<script>
var f = new ActiveXObject("Scripting.FileSystemObject");
var name = '\\\\TheServer\\Users\\Public\\Downloads\\test.txt';
if (f.FileExists(name)) {
var stream = f.OpenTextFile(name, 1);
var text = stream.ReadAll();
stream.Close();
alert(text);
} else {
alert('File could not be accessed.');
}
</script>
</body>
</html>