No, you don’t.
All your designs are stored locally on your Mac and most features are accessible without an internet connection. You only need one if you want to view the linked YouTube videos, blog articles, etc., or import or export from third-party apps such as iCloud, Google Drive, and Dropbox.
If you have a Shapr3D account, make sure you log in to your account in the app before going off the grid. You’ll need web access for your account to be authenticated.