It's all about context. When you're alone at home and have no access, let alone be inclined to reach out to anyone all you have is willpower. It's essentially a short term .. I can't call it a strategy, but it has it's place - and it's a fairly small one.
I think that's a different question from quitting cold turkey, if we define cold turkey as simply continuous abstinence. You can have all kinds of support and have continuous abstinence of whatever length. But if you understand cold turkey as just trying to do it all yourself, total abstinence from an arbitrary point in time with no support system at all then your chances are not good.
Actually, the internet itself and even subtler, cultural collective patterns of thinking is like a supportive network, and is in that sense a context. Unfortunately the mainstream culture largely works against us in many ways so it's supporting something, but not your effort to quit. And personally I've found the, shall we say ready-made recovery networks a bit wanting and not necessarily very sophisticated but I think there's also a time and place there and a lot of people can get something out of it.
The basic question is what in the collective context can you use to your advantage? When I say support system I don't just mean a social one where you have people on a list or something, even though that's a part of it. But if there's a system there's a matter of understanding and a matter of details. I think if you can get a good number of people together and actually think systematically, not repeat stuff from a program (and not even relate to it as a program) but actually understand how a program in the general sense of the word works, that's where the rubber meets the road. When there's no interest in a systematic approach it tends to be a matter of show and tell only. Abstinence is a general condition, including abstaining from internet access but that's not really a systematic understanding of anything and not the only variable. It would be a bit like only ever thinking about fasting when you're working on your diet. Yeah there's intermittent fasting and stuff, but the content of your diet and other specifics are important. And while some things are ultimately possible to abstain from indefinitely, maybe the better question is what are things you can't abstain from, and what are the details of working with those things? It's way too tunnel vision to look at abstaining from the bad stuff or the one bad thing you are trying to quit, and that approach ignores context.