If your cookies are configured correctly the cookie is destroyed.
I recently helped a user who was wondering why logout was not working for his phpbb integration
Come to find out his forum is setting his cookie .domain.com and in Photopost he had it set to blank which was
www.domain.com so when he logged out of Photopost it was not blanking the forum cookie.
If things are aligned properly in every one of our integration we set all cookies we use to blank and expire them