No. The project existed almost entirely on paper (a very small-scale experiment using high-explosives was conducted). It died out with the Limited Test Ban Treaty (no atmospheric nuclear testing, 1963), and would become totally impossible under the Outer Space Treaty (no nukes in space, 1967). To actually develop large-scale Orion-style craft would also be incredibly resource-intensive, and there has never been enough political or military will for that sort of thing (even a program as relatively modest as Apollo was only mildly popular amongst Americans at the time, despite our retrospective valorization of it).

On the history of Project Orion, George Dyson's Project Orion: The True Story of the Atomic Spaceship remains the definitive source.

It is interesting to consider what kinds of social or global conditions would lead a country or world to invest in such technology, but this remains in the realm of speculative fiction, not history. (Neal Stephenson's fictional Anathem probes this question.)