Doubling the number of thylakoids is expected to result in increased photosynthetic efficiency if all other photosynthetic resources are available adequately. However, the actual improvement in efficiency may be limited by other factors and potential cellular constraints.
Doubling the number of thylakoids would theoretically result in an increased photosynthetic efficiency because thylakoids are the structures within chloroplasts where the light-dependent reactions of photosynthesis occur. More thylakoids would mean more surface area to capture light and produce the energy carriers ATP and NADPH, which are essential for the Calvin cycle, where carbon fixation occurs. It is crucial to note that this increase in efficiency assumes that all other factors required for photosynthesis are present in adequate amounts.
However, one must also consider that simply having more thylakoids doesn't guarantee increased efficiency if other limiting factors are present, such as insufficient light, water, or carbon dioxide. Moreover, packing too many thylakoids into a chloroplast could disrupt the process if it leads to overcrowding and impaired functioning of the photosynthetic machinery.
The most likely answer is that doubling the number of thylakoids would lead to increased photosynthetic efficiency, provided that the plant's overall physiological and biochemical conditions are optimized to support the additional thylakoid membranes.