No, the Moon does not play a significant role in slowing down the Earth's core rotation and creating the Earth's dynamo. The Earth's dynamo is generated by the movement of molten iron within its outer core, creating a magnetic field.
The Moon's gravitational interaction with the Earth primarily affects the tides and causes tidal forces, but these forces are relatively weak when compared to the forces generated by the Earth's internal processes. The rotation of the Earth's core is primarily influenced by convective currents driven by heat flow from the core to the mantle, as well as other factors such as the Earth's overall angular momentum.
While the Moon's gravitational influence does cause a slight transfer of angular momentum between the Earth and the Moon, this effect is more noticeable in the orbital motion of the Moon rather than the rotation of the Earth's core. The Moon's tidal forces lead to a gradual lengthening of the day on Earth, but the effect is very small, with the lengthening occurring at a rate of about 2.3 milliseconds per century.
In summary, while the Moon does have some influence on the Earth's rotation through tidal forces, it is not the predominant force responsible for slowing down the Earth's core rotation and creating the Earth's dynamo. The Earth's dynamo is primarily driven by internal processes within the planet.