At no point was Fuchs an American citizen. As he was, at the time, perhaps the leading theoretician on plutonium implosion; it seems more logical to argue that without Fuchs it would have taken the Americans much longer, particularly as all the devices, other than Little Boy (a dead end, but relatively reliable and simple) used plutonium implosion.
It is now generally agreed that the American's curtailing of newer information to the British (from July 1942 through 1943) probably delayed the Los Alamos project by about a year, as it was still heavily reliant on Tube Alloy theory and research. The British work was heavily constrained by a lack of resources caused by waging war against Germany from 1939. Obviously the wealth, engineering expertise, and organizational ability of the U.S. were the main reason for the success of the Manhattan Project, but it would not have existed without the fundamental Tube Alloy work. Fuchs and other Soviet agents were at least partially responsible for the reduction of trust of the British by the U.S. after the war. Although U.S. nuclear test data was generally shared, relatively little cooperation occurred on fusion weapons.