Yes it can! This is a significant security improvement.
The safe mode limits PHP to be able to perform actions only on files/folders who's owner is the same as PHP is currently using (this is usually 'apache'). As files normally are created either by the Joomla! application or by FTP access, the combination of PHP file actions and the FTP Layer allows Joomla! to operate in PHP Safe Mode.
Don't use a module class suffix and your mods will be plain like this.
Style the search like above. Just use the module class suffix of "search"