I have tried editing the format of password protected page and it was successful. But my client asked if it's possible to change the format of the password protected page using the Visual Editor in WordPress admin.
I am hoping for your immediate reply, thanks!
Short and simple answer is no. I've been using wordpress for a long time and there is no readily available plugin or method to do this that doesn't involve a lot of custom coding.
The closest that I know of is the plugin WP-Admin Theme plugin. But it seems to be quite old. There are probably others but I believe they are geared more to CSS overrides than using the in-built wysiwyg editor of worpdress. This means that your client would need to know some basic html and css in order to use it.
For more information on creating admin themes there is some Wordpress meta: http://codex.wordpress.org/Creating_Admin_Themes
I don't like to plug for pay products but I also did find this: Tailored login from I-Themes. However if there is a commercial product i'm sure if you search the WP plugins database hard enough you might find a free product that is similar.