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No, it isn't necessary to assign contexts to your projects. If you don't like seeing them in the context view, you can either adjust your view to only show Available actions (only projects with nothing left to do will appear), or use View->Hide Parent Items in Context Mode to suppress them.

If you don't wish to hide parent items in general, and have a project which will be empty but you still don't wish to see and don't want to assign a context to it, you can create a dummy action with a start date a few years in the future in that project. The presence of an uncompleted action will keep the project from showing up in a list of Available items, and the future start date will keep the dummy action from showing up in your lists of Available items.

If you want some background on why projects behave this way in the context list, this thread discusses it: