This will only get big if they can be quick to implement improvements. One of the things that's made PUBG so successful for me is just how quickly it has been updated in early access, and if Fortnite can garner that same momentum it will definitely be big.
Improve gunplay, improve loot, increase speed on gas so you can't outrun it, improve UI so that you don't pick-up guns to replace your main as easily and add first person mode. Do those and you'll have a bloody good free PUBG.
Also unless I'm mistaken the team that worked on this mode was the team behind unreal tournament correct? They'd have moved on by now so no doubt it is being moved into internal development and thus I can see where some concern is coming from. But hey, if people play PvP more then that just means the PvE doesn't have the right hooks.