Possibly, depending on what services the cloud services company provides.

Section 7(c)(2) of the Bank Service Company Act (12 U.S.C. 1867) requires banks to notify their supervisory banking agency within 30 days of any contracts with a technology service provider that provides certain services, including the following:

… check and deposit sorting and posting, computation and posting of interest and other credits and charges, preparation and mailing of checks, statements, notices, and similar items, or any other clerical, bookkeeping, accounting, statistical, or similar functions performed for a depository institution.

Broker-dealers need Financial Industry Regulatory Authority approval for first-time usage and subsequent notifications of changes or additions, but there are also additional process-based steps.

Investment advisers do not need to notify the regulator about outsourcing. 

With respect to entities regulated by the Commodity Futures Trading Commission ("CFTC")/National Futures Association, there is no explicit notification requirement regarding cloud service providers. However, the rules mandate a process through which each CFTC entity must adopt an information systems security program, and each information systems security program would necessarily address the use of cloud service providers.