if (!$.cookie('client_email_cookie'))
only checks to see if the cookie exists, it doesn't check its value.
$.cookie('client_email_cookie')
returns the value of the cookie (in your case email
). Compare that value to the email that was entered to see if it has been registered.
Also, not to state the obvious, but this can be easily defeated anyway by the user simply deleting the cookie if they so desire, registering from a different browser or computer, using private browsing, etc...