Only if bitstamp wanted to hurt their reputuation with no upside for them. "Hey potential customer, don't worry your personal info is completely safe, unless random people on the internet want it." 
Bitstamp must follow the data protection laws of it's country, or face prosecution for revealing a customer's personal details. Also, that particular customer can now afford the services of the best lawyers in the world to sue on his behalf. I doubt Bitstamp will tell us who the whale is.