If the Devils are on TV in his/her local area, they will be blacked out.
This is pretty much the right and most simple answer. With Gamecenter, if you live in Jersey or New York, you will never get a Devils game because it's always available on some cable network (MSG, MSG+, NBC Sports, NBC). Cable gets first dibs. I believe Center Ice works the same way, but since that's a cable platform, it's really only useful for watching out or market games. Same with Gamecenter.
I live in Austin, TX, so Gamecenter works great for me. I get every Devils game except for Devils / Stars and if they're ever on NBC or NBC Sports.
Just an FYI, Gamecenter stinks during the playoffs. You'll only get about half of the first two rounds and none of the finals, because NBC Sports and NBC has a good portion of the games. You'd think the NHL could work out a deal that would make the Stanley Cup Finals available on every platform, but that's not the case.