If you buy the game digital then yeah most likely you would be locked out if the server crashes although for some reason the last time it happened everything still worked i just couldn't access the playstation store.
and i mentioned having issues with Arkham knight but i kind of blamed the wrong people there... turns out it was just a glitch that was patched.
atleast when the psn server isn't working you can still use most apps like netflix or wwe network.
^ That's exactly why I don't trust digital downloads. I only ever download digitally on the PC.
Off topic, but I also find that my PS3's WWE Network runs a hell of a lot smoother than on Google Chrome on my PC.

Thanks Taker_2004 for the banner!
I was under the impression that digital downloads on PS consoles will still play if there's no internet access, but only on the primary device. People who have more than one PS in a family who use the same account wouldn't be able to play them with no internet, unless they're using the primary device. Could be wrong though, but that's what a mate told me a while ago.
Ben... that seems very logical actually, as i have some of these games downloaded on my profile on my brothers ps4 as well... i never set any console as a primary one.
I don't play online, but wasn't the issue that you have to be connected to play even offline?