Yes, sort of.
It sounds like you are thinking Fortnite is a normal MMORPG, and it isn't.
There are two modes in Fortnite: Campaign mode, and BattleRoyal Mode. Most people think of Fortnite now refer almost exclusively to the BattleRoyal mode, which was tacked onto the original game when Campaign mode started failing and PUBG picked up.
Campaign mode aka "Save the World" is a series of co-op maps where you can have a party or random players join you for a little Player versus Zombie action. There is a solid progression in this one, and you have an 'explorable' base, but it is only used for a couple of specific missions. You see all your allies on the map at all times.
BattleRoyal mode is also an instance based game. In this one you cannot see anyone on your main map, but allies appear in your mini-map. (Markers allies put down also appear on the main map.)