While some games will NOT work without an internet connection (due to some annoying DRM measures), most games will work with minimal issues.
TO access your Steam games & games on other digital distribution platforms, you'll need to engage OFFLINE mode after getting the latest updates online. Please be aware that you will need to get your computer online every so often (between 7 & 30 days) to confirm you still have the rights to the games in your library.
For GoG.com titles, being DRM Free, you can download, install & play them with minimal issues while offline.
Please be aware that some features, like cloud save support, will not be available while offline. Therefore, you might want to try to get those in-sync before going offline.
Hope this helps!