Designing a fission nuke isn't as hard as people like to make it out to be. With a couple of math and physics students and access to unclassified materials and you can have a working, though perhaps not efficient, design in less than a year. We know this to be true because someone paid a couple of graduate students to do it and they came up with a design that, according to analysis by experts, would have worked. He might have helped them along by a few months, but the real bottle neck in any nuclear program is the enrichment process.
Fusion bombs are a bit trickier, but Fuchs left the US program before the difficult parts of the problem were fully understood. Again, he might have saved the Soviets some time, but would 6 months or a year really have made that much of a difference in history?
The only conceivable way I can imagine it changing history is if the US, emboldened by being the only power in the world with the H-bomb, had used them almost immediately after the outbreak of hostilities on the Korean peninsula. Not as far fetched as it may sound, there were voices in the US military who were calling for the nukes to be dropped even with a thermonuclear capable Russia right next door. Without that threat they may have gotten there way.