The Soviets did thermonuclear research alongside their fission research, and assumed the Americans were as well (and they were right about that; the Truman "crash order" added a little urgency and priority, but the US was already working on H-bomb stuff since World War II). They benefitted from accurate espionage-derived intelligence on the state of US thermonuclear intelligence through around 1947, and were pursuing the same things, more or less, as a result. It was not a "crash" program, per se — it was just part of their normal research activities. They did not figure out how to make multi-megaton thermonuclear weapons until after the US had detonated one of their own, however.

So one could make the argument that if the US had held off, and made it somehow clear that it was going to hold off, that the Soviets might not have been as rapid in their development. However given the lack of any way to verify if someone was researching thermonuclear weapons (other than a full-scale test) it seems unlikely that the Soviets would have taken any agreement very seriously (whether the US would have would have depended on how it was passed down). The Soviets, at least in their later years, generally regarded any verification-less treaties to be by their very nature likely to be violated on the US side, and so felt free violating them themselves. They regarded unilateral moratoriums (like the Test Ban Moratorium from 1958–1961) as being worth following only as long as it fit their interests (the US has held similar attitudes over the years).

Is it possible that if the US had not raced into detonating a full-scale thermonuclear weapon that the Soviets would not have hit upon the way to do it? Often seeing that something is achievable is very stimulating to the imagination, and there are some allegations (denied by the Soviet scientists) that they were able to analyze the fallout from the US test to derive information about its design. So I guess you could imagine the whole thing being dragged out a bit longer if the US had pushed for such a thing.

But I think it is very unlikely that the Soviets would have agreed to a "true" moratorium on the research. They would have needed to know if it was possible. Them being without thermonuclear weapons would be a significant disadvantage — more so than the US being without them. Why? Because the US had access to many forward bases and allies next to the Soviet Union. That meant that they could effectively attack the Soviets even without intercontinental ballistic missiles, with huge waves of bombers. The Soviets could not effectively do the same thing to the United States; it is too far away, and bombers are too vulnerable. This is why the Soviets invested, from quite early on, in ICBMs. And early ICBM accuracy is low-enough that anything less than a thermonuclear warhead is not an effective deterrent. (The US did not really begin investing in ICBMs until after it had thermonuclear weapons, for this very reason.)

All of this is speculative, of course. I respect Priscilla quite a lot as a scholar and a person (she has had an amazing life — look her up!). There was an interesting article written by weapons designer Herbert York in the 1970s that essentially argued that even if the US had not developed the H-bomb and the Soviets had not changed their history at all, that the US would not actually have been at any significant disadvantage and would have likely been able to "catch up" almost immediately. Which is to say, that the US had very little to lose from a moratorium attempt. So that is another position. (For this, see the discussion here.)

But I think the view that the Soviets would have held off on H-bomb work both underestimates the Soviet view of things, and also underestimates how attractive the H-bomb would be for Soviet deterrence purposes. The US could effectively deter without the H-bomb; it is not clear the Soviets could.