They get it all anyways when Theodore Hall offers his services on his own volition.
Assuming that doesn't still happen for what ever reason, the common estimates is that espionage accelerated the Soviet program by a minimum of six months and a maximum of two years. In one way it actually benefits the Soviets in that they can lead with a more efficient and powerful domestic design instead of a identical copy of the Trinity device that they settled on for OTL.
"Implementing the stolen plans still required immense technical skill and a deep understanding of atomic processes. In addition, though the information was, as Ioffe claimed, always precise, Soviet scientists could not assume that it was. An immense amount of checking had to be done, since it was always possible that the Americans had intentionally released carefully constructed disinformation. And, in order to protect the secret of the stolen secrets, only the most senior scientists were aware that the designs had been pilfered. Most scientists went to their graves believing that their bomb was distinctively Russian." -
The Bomb: A Life, Page 128.
"Fuchs himself did not believe that his contribution was crucial. In his interrogation, he remarked that he was 'extremely surprised that the Russian explosion had taken place so soon'. In common with other [Western] analysts, he had assumed that the information he had given 'could not have been applied so quickly and that the Russians would not have the engineering, design, and construction facilities that would be needed to build a production plant in such a short time.'" -
The Bomb: A Life, Page 147
"Beria was not remotely moved by the ideals that motivated his scientists. He was not an esoteric voyage of discovery but a practical quest to build a bomb in the shortest possible time. Therefore, he simply told his scientists to build an exact copy of the American bomb, the specification of which had been supplied by Fuchs and others. A specifically Russian design was cast aside even though it offered more promise than Fat Man.[Footnote here, when going to the bottom of the page to read it, it says:] When finally built and tested in 1951 (the second Soviet atomic test) it produced twice the yield, at half the weight." -
The Bomb: A Life, Page 135.
Contrary to popular belief, there was no concrete "secret" behind the atomic bomb. The discovery of fission in 1938 meant that a nuclear chain reaction was possible and that the energy produced from this process could be used to produce a weapon of unusual force. Physicists like J. Robert Oppenheimer, Enrico Fermi, and Leo Szilard knew that it was only a matter of time before other countries were able to develop their own atomic weapons. The only secret behind the bombs lay in their specifications, material composition, and inner workings. Any government with the determination and the resources to develop an atomic weapon could do so within a matter of time.
When Klaus Fuchs's espionage was discovered in 1950, many believed that his actions had been essential to the Soviet bomb. Fuchs did pass along important information about the bomb's design and technical specifications, and the Congressional Joint Committee on Atomic Energy concluded that "Fuchs alone has influenced the safety of more people and accomplished greater damage than any other spy not only in the history of the United States but in the history of nations." However, there has been much debate surrounding the role of espionage in the Soviet Union's atomic program. Scholarship suggests that Soviet spying probably allowed the USSR to develop an atomic bomb six months to two years faster than they would have had there been no espionage.
-https://
www.atomicheritage.org/history/soviet-atomic-program-1946 (Emphasis added)
They were able to skip a couple years of lab tests and experiment design.
No, they still had to do a whole bunch of those in order to verify the information they had been getting.
IIRC it was the development of the Hungarian Uranium deposits post 1946 that initially fueled the Soviet atomic energy programs. By 1954 the mine workers were a factor in the Hungarian revolt.
Most of the uranium came from mines in Central Asia which had been under development since 1944. Smaller portions were sourced from Eastern European countries like East Germany, Czechoslovakia, Bulgaria, and Poland but Hungary does not show up as a source on Soviet import lists from this period.