PS4 Pre-Order Download, Disk Required?

Hello, I like to use remote play a lot and sticking a few games on the Hard Drive makes it easier when away from home to connect my Vita and play a range of games. I was hoping that when I get the disk for the game that I would not be required to put the disk in, in order to play? I'd like to have it HD only so I could put one of my other disks in so I have other options... Anyone happen to know about the install options?

I pre-ordered the game, but, downloaded it on my PS4. I was emailed my code, so there isn't any need for the DVD. I just put the code in the Playstation store "redeem code" at the bottom of the screen and that was it.

I did as well, I just wonder if the download was complete or just enough for early access.