Answer
No, the cooking time is the same.
Work Step by Step
Boiling water, whether it is vigorously boiling or gently boiling, has the same temperature (at a given pressure).
When spaghetti is cooked in vigorously boiling water, it moves more, and is less likely to clump together or to stick to the pan - but it takes the same amount of time to cook as it does in gently boiling water.