He passed on a great deal of highly technical information, it wasn't napkins. It probably helped the Soviets get to a working weapon faster but it's generally accepted they'd have got there without the espionage as well.
It would have taken them longer. They might have learned of the dangers of radiation from research rather than after causing unbelievable nuclear pollution. Or from the American experience once the dangers of radiation were well publicized later (though that might not have happened without a nuclear arms race).
