Help needed! Can I can continue to play with the same disk, on a new PS4?

Hey all! I'm housesitting for a few days, and it's impossible to bring my PS4 with me, but the house has a PS4 there already! I've just started Heavy Rain, and don't want to have to start again on this new console. If I bring the same disk, and log into my account, will the data still be there?

It's obviously not detrimental, I suppose I can wait a few days before playing (not that I want to). I'm a little tech incompetent so excuse me if this is a silly question!