Rename image during upload using date and time stamp?

You could e.g. check the filename and extension from the pathinfo, after your custom sanitization.

Example:

If the filename is empty and extension non-empty, then add the formatted current time as the filename part:

$info = pathinfo( $file['name'] );
if( empty( $info['filename'] ) && ! empty( $info['extension'] ) )
    $file['name'] = sprintf( '%s.%s', current_time( 'Y-m-d-H-i-s' ), $info['extension'] );

If the file áéíú.png is stripped to .png with your custom sanitization, then it would be renamed to 2016-08-14-10-54-07.png

Note that if you import another such file within the same second, then wp_unique_filename() will add -1 to the filename part so it will be renamed to 2016-08-14-10-54-07-1.png. The third file would get -2 appended and so on.

Hope you can adjust this further to your needs.