Thinking through the different modes of heat transfer with a pot of water boiling, there are two primary drivers.
- When the pot is placed on a stove burner, conductive heat transfer occurs as the flames/electric coils of the burner interface directly with the bottom of the pot.
- As the water comes to a boil, heat from within the moving water is transferred via convection. Boiling water is the moving fluid in which heat is transferred to the pasta.
To answer the question posed, it’s important to define what “cooked” pasta means. The primary reason to cook pasta in boiling water is for accuracy and reliability in cooking times. Boiling water is guaranteed (not accounting for altitude) to be at 212 F (100 C). With a set temperature you’re able to cook with a very high measure of confidence.
Regardless of the amount of heat applied via the burner, excess heat applied to the body of water is converted to steam while maintaining a boiling temperature of 100 C.
In the case you add pasta before water begins to boil, it will begin to cook before reaching the boiling point. To maintain the same level of reliability, you’d have to check the temperature and empirically assess when the pasta is “done”.
If I were to make an assessment, I’d answer by saying you can have “cooked” pasta faster by adding it before water comes to a boil, however, you’d lack consistency in terms of the actual end product of what “cooked” pasta is