No update required.
@kokokko416 support is on the disc.
— Drew McCoy (@DKo5) October 23, 2016
So all you need to make room for is the whopping day one patch of 88MB. Vince Zampella shared the good news on Twitter last week, so if you have a crappy internet connection, you won't have to worry.
Titanfall 2 is the first title that we know of to have PS4 Pro support on the disc. There are still a number of unreleased titles to come with PS4 Pro support but I imagine we'll hear more on those closer to their release dates.
Titanfall 2 is out for PC, PS4, and Xbox One this Friday, October 28.