It is hard to know how to measure such things, but I think one can say that Groves had a fairly detailed understanding of the big issues that stood between him having atomic bombs and him not. He understood what enriching uranium and what making plutonium involved. He understood the work of making the weapon itself. He could not have done that technical work himself. But he seems to have gotten details that one could count as a fairly good understanding — he knew, for example, what Xenon poisoning (a type of reactor flaw) was, what its implications were for the US program, and its value as a "secret" (that if you didn't know it was going to happen, then you wouldn't plan for it). Did he have a detail understanding of cross sections? Probably not. He leaned heavily on several scientific advisors (Oppenheimer was the most famous person he worked with, but his day-to-day science understanding came more from people like the physicist Richard Tolman, who could translate it into something Groves understood more readily, and were more independent than Oppenheimer).

The reputation amongst the scientists was that Groves was a dolt, but that seems based more in professional irritations with his style and manner (and perhaps, appearance) than reality. He was not a dolt, but he was also not an academic scientist.