Yes, I think so. That research is already public or available on the black market anyway, and the US built the first nuclear bomb ~70 years ago, so it's kind of a moot point.
But what would the alternative be? That only the governments which discover how to build a nuclear bomb understand how it works and what its effects are, and get to threaten the rest of the world with impunity?
I'm not certain that would be better than the world where everyone at least understands the underlying science, even if not everyone can build one.
There's a big difference between the nuclear bombs countries with nascent nuclear programs (like North Korea) can build, and those the US can build. So unless you're talking about just enough knowledge to build the simplest of nuclear weapons, it's far from moot.
Everyone does understand the underlying science (or can find it pretty quickly on the internet), but very few understand the engineering specifics.
That information is harmless without the resources to do anything with it. Nonproliferation is targeted at resources, not information for this very reason.
But what would the alternative be? That only the governments which discover how to build a nuclear bomb understand how it works and what its effects are, and get to threaten the rest of the world with impunity?
I'm not certain that would be better than the world where everyone at least understands the underlying science, even if not everyone can build one.