At the moment, the only way to play games while appearing offline is to simply not sign in to one's profile, enable offline browsing, or disconnect from the internet, but then any online experiences will be unavailable. For some games such as Fortnite, players can find an option under the main menu to set themselves as a way, in a private party, and turn off notifications for friends. The closest thing to being invisible online is the "do not disturb" feature, which is truly not the same.