It is a good idea to save all cloud-stored documents before signing out. The OneDrive app login is separate from the Office/Microsoft 365 login. However, it’s possible to work with documents synced to the local computer.
Most obviously, direct OneDrive access isn’t available. Some cloud-based features only work with a Microsoft account login. Microsoft’s warning message, see above, says “To complete the process, close all Office apps.” But if you keep the programs open after sign out they’ll still work.