No, it is not required to install Business Analyst Desktop to integrate Business Analyst local data with ArcGIS Pro. Since the Business Analyst extension is in the ArcGIS Pro codebase, all Business Analyst tools and capabilities are enabled through licensing, and there are no additional installation or setup required. Users are also not required to download and install the Business Analyst local data from My Esri if their ArcGIS Pro is connected to an ArcGIS Online organization or the Business Analyst Server of the organization.
Note: Unlike ArcMap, the Business Analyst functionalities in ArcGIS Pro are geoprocessing tools instead of wizards. To avoid using service credits after installing and licensing Business Analyst data, set Data Source to desktop in the tool environment. For more information, refer to ArcGIS Pro: Data Source (Environment setting).