Negotiations and threats? I don't think so.
Let's assume the nuke is used in the East. The Soviets take 10,000 casualties (for a tactical use; or much more, but on civilians, if the Germans manage a strategic delivery). Given Stalin's attitude towards casualties, and the fact that any negotiated peace would be felt by him as leaving the wolf alive and well on his doorstep, the Soviets are not willing to negotiate. On the other hand, why should the Westerners negotiate? The price has been paid by the Soviets, and it's likely other bombs will be used in the same place. No problem with Churchill for sure.
Now let's assume the nuke is used in the West. The Westerners are much more sensitive to casualties. Then again, they are those who are about to have their own gadgets, so they will feel much less helpless. And because they know exactly what is the potential of those gadgets, their priority number one will be making damn sure Hitler is not left alone with an undisclosed number of those toys. Better push ahead now, take any further losses, and clear up Germany for good.
Of course, much depends on the time frame. April 1945, somebody said. That's when some vanguard US units were already marking time, in order not to have to fight for territory that would be handed over to the Soviets. The advance in Bavaria was neither top priority nor top speed. If the bomb is used, then all of that changes, and it's likely that the German site is overrun even before the second bomb is dropped