Out of the box on most consumer networks, you're going to be able to access things like the store, downloading updates etc.
To play with certain players on peer to peer games (which are less common these days) or have a voice chat with certain players, you will need to port forward (manually or with UPnP).
You either need to forward ports manually (which can obviously only be done to one console), or use UPnP. The Xbox One and later does have an option to manually ask it to use a different port on multiple consoles for some features (so that you can port forward separately to consoles), but I am unsure if that will solve all issues in such an environment.