Only if they can prove that the cloud company are providing access to their own employees or to third parties without getting permission from the account holder - and the account holder would in turn need to get permission from each affected person.
More worrying is the other case, in the USA, where the US courts are saying that it is irrelevant if the data in Outlook.com is held on servers outside US jurisdiction and the servers are owned by a company not incorporated in the USA (MS Ireland), MS USA is incorporated in America and is the parent company and "it is only data", so the USA has jurisdiction in Ireland to obtain the data with a US search warrant.
If MS lose the appeal, then it will effectively make using any cloud service with ties to the USA unusable, because you could face prosection at any time in the EU for violating the Data Protection laws, when the cloud provider hand over non-US data to the US Government without getting a valid EI warrant.
Biting the hand that feeds IT
