Is it possible? Certainly. Is it likely? I don't think so. Its not the density of the population so much as it is the density of attitudes.
People being able to take care of themselves has been mentioned, and I think that's the telling factor. Now, I won't argue about how virtually none of us could survive (let alone live to even close to current standards) without other people. That's a red herring.
I think the difference is that rural people understand that being able to take care of yourself is the ideal, and the expected standard. Yes, we don't all grow our own food, we shop at the markets, but a high percentage of the people understand what it takes to do it, and many could if they needed to.
Likewise taking care of other things, like personal protection. Because there is seldom anyone else around to do it.
In the major urban areas and inner cities, we have huge numbers of people who have been taught since birth that its not their job to take care of themselves, it is the job of their govt. In ALL things.
The people in the govt want to take care of them, and its always easier for the govt to do that when the populace is disarmed.
Sure, it's an over simplification but essentially we have major cities of grasshoppers able to live as they do because of the rural ant farms.
I think any right to arms beliefs in a hyper crowded society would probably be a sci-fi story secret society. A tiny minority, "worshiping" in secret.
Consider that even when not a democracy, what the mass of the population believes they want, they get. And in a world of shoulder to shoulder people, believing you have the right to be armed, and defend yourself is an intolerable expression of individuality.
Mankind, in general (and look around the world there's plenty of proof) only allows that kind of individuality on the frontier, not in the civilized cities.
Also prevalent is the attitude or belief that "the nail that sticks up, gets hammered flat".
Look at all the fine work they have been doing, with ever greater results in the last half century. Guns are evil, bad, dangerous, only used by criminals and the deranged, etc. Only a uniform or a badge can protect good people from the corrupting influence of the gun, having a gun as part of your job is the only way you can keep from being turned into a raving mass killer. ETC.....
This is the mantra, repeated endlessly. The Big Lie. When there is no counter allowed, it does work...