If you were already logged in (on PS4 not PC) before the issues started then you would not be effected. It's not really an internet connection issue though but more the medium (in this case PSN) couldn't be reached, preventing logins and whatnot. Essentially it's like if Steam went down and you couldn't access certain games, pretty much a similar thing with PSN. Most PSN outtages don't last very long though so this recent one was unusually long, perhaps someone was sad Sony wasn't at E3 and DDOS'd them...