Check if email address exists front end with AJAX in a plugin

I’ll guess that you’re testing this by entering your admin email address. Have a look at the Codex page for email_exists():

If the E-mail exists, function returns the ID of the user to whom the E-mail is registered.

If you’re entering the email address of the first user created for a site, the user ID will be 0, so if ( email_exists($email) ) for that user will evaluate false. The example given on that page does not account for this situation.