On non-CICS, you are not required to upgrade existing VS COBOL II programs to Enterprise COBOL to run them under Language Environment.
You might also want to upgrade your OS/VS COBOL or VS COBOL II programs if you want them to use Enterprise COBOL or Language Environment features (such as Language Environment callable services, intrinsic functions, or running non-CICS COBOL programs under more than one task in the same address space under z/OS).