Total dark deprivation at day-neutral plants
I cannot say anything about the general case, or specifically for day-neutral plants. However, Sforza et al. (2012) have studied the effects of light conditions on algae (used for biofuel production), and their results indicate several problems with continuous light. In continuous light conditions they find lower chlorophyll contents and higher carotenoid concentrations in cells, which leads to lower photosynthetic efficiency.


This figure shows chlorophyll contents (black) and chlorophyll/carotenoid ratio (red) under different conditions, with the two treatments to the left representing continuous light. (graph from Plos One)


  Results show that Nannochloropsis can efficiently exploit even very intense light, provided that dark cycles occur to allow for re-oxidation of the electron transporters of the photosynthetic apparatus. If alternation of light and dark is not optimal, algae undergo radiation damage and photosynthetic productivity is greatly reduced.


However, they also experiment with pulsed light, which in some cases lead to even lower rates of photosynthesis:


  However, similar experiments, at different frequencies, also showed that alternating dark and light may be detrimental, as demonstrated by the growth inhibition observed in the 1200-1 and −5 Hz curves. These cells showed a decrease in Fv/Fm values similar to that observed under constant strong light, indicating that the inhibition of growth was due to photoinhibition.


They also find that light pulses can be very short, and still allow for the photosystem to reset:


  The optimal duration of light pulses was found to be around 10 ms, which is consistent with the suggested PSII turnover rate in whole cells [4], [46]. Accordingly, after photon absorption by the photosystem, 1–15 ms are needed to reset the system, before it is ready to receive another photon [22]. If the illumination is this short, most photons are exploited for photosynthesis and do not lead to the formation of ROS which then causes photoinhibition. These results indicate that even strong light does not cause damage if it only lasts a short time. Conversely, longer exposure allows the generation of ROS and damage and, in this case, the abrupt changes in illumination undergone by the cells are as harmful to the photosynthetic apparatus as constant high light.


Different species of plants can have mechanisms to handle light stress in different ways, so the effects on different species and types of plants are likely to differ. However, their results should generalize to some extent/for some plant species.

You may also find this paper by Li et al. (2013) interesting.