Since Visual Studio only runs on Windows, Enterprise Developer for Visual Studio only runs on Windows. You can use Enterprise Developer for Visual Studio on Windows to develop COBOL applications to run under Linux. It's not clear to me what you want to do.

Enterprise Developer lets you develop COBOL applications for Windows and various Unix and Linux platforms. Enterprise Developer for z/Enterprise lets you develop mainframe applications on Windows, for deployment on the mainframe or under Enterprise Server. (There's also Enterprise Test Server, which lets you test mainframe applications locally before deploying to the mainframe.)

With Enterprise Developer for Eclipse, you can use the Eclipse IDE on Windows to build and debug COBOL applications on a remote Linux system.