The answer is "No", these folders contain information about what is being installed hence should not be deleted. If deleted, it will throw errors when trying to install the next BO patch. It also contains records of the files that are associated with each Business Objects installation on the system (e.g. WAR files, DLL files). Software Inventory Tool also uses the Cache folder to monitor changes made to a system's Business Objects software via Business Objects' installers for original installs and updates, including Critical Hot Fixes (CHF) and Service Packs (SP).
[BO XI 3.1]
Delete the logs inside the <Install Directory>\Business Objects\BusinessObjects Enterprise 12.0\Logging Folder
Delete the logs inside the <Install Directory>\SAP BusinessObjects\SAP BusinessObjects Enterprise XI 4.0\Logging Folder.