You're creating a strawman. I can't see why Github would make the mistake you believe they'd make as they don't have the self-interest that Facebook and Twitter have in killing your focus with an onslaught of notifications.

I think you could expect all forms of notification to be hidden by default.

It would actually likely improve your ability to concentrate. You would be able to switch into another mode of a developers workflow without needing to context-switch onto an often focus-distracting browser.

Anyway, my core point was that there are a combination of features that allow the creation of a new holistic programming experience. I am not arguing its correctness and I am not arguing that it would suit everybody. :)

Exactly - making context switches cheaper isn't very helpful if you're doing so at the expense of making context switches more frequent[0].

[0] and easier to do "by accident"

This is a silly argument. You're all assuming this type of integration will be have the UI quality of your dishwasher.

Of course context switches and irrelevant information will be distracting if done poorly. This is a UX challenge—not a reason to abandon the idea.

Having the focus you need during concentrated tasks such as coding, while also enabling the integration of other tasks—such as high-level team context awareness and collaboration—is the key design challenge. Done well, it would be a killer app.

Done poorly, as with anything, it will fail miserably.

Programmers have a poor reputation for UI design prowess, and programmers tools are sadly usually made by programmers, and thus carry the same reputation. Very few amalgam programmer/designers exist to bridge the gap of motivation and ability to design a better toolset. But they do exist.

Let's be optimistic, shall we?

They're not quite the same. Those are push-notifications. Push/pull is orthogonal to what application you use for which purposes, especially if you have a desktop were you get such push notifications thrown at your peripheral vision no matter what application you're in.