If you are going to research "polyps," be sure and not confuse the many different types of the word. Polyps of Z&P are colonial anemones, star polyps are different than polyps on LPS which are different than on montis or on birdsnest or on acropora.
...or polyps on a NPS which do need to exchange gas even more since there is not photosynthesis but also need to catch a lot of food.
Well, we are talking about the genus Acropora specifically when it comes to nocturnal axial corallite extension so -
"As sessile organisms, coral behavioral changes include polyp and tentacle extension and
retraction, which often display diel patterns (Levy et al. 2006). Tentacle behaviors, which may help
the animal avoid predation while maximizing photosynthesis, heterotrophic feeding and gas
exchange (Levy et al. 2006), appear to be light-responsive, but may also have a circadian
component of regulation (Tsang et al. 1997; Levy 2003). In some corals, such as the Caribbean
Acropora corals, tentacle behavior varies between different parts of the colony (E. Hemond & S.
Vollmer, personal observation), suggesting complex regulation beyond uniform light-response.
Tentacles of Symbiodinium-rich radial polyps throughout most of the colony are extended during
the day to capture light and remain extended at night, while axial polyps at the tip of the branch,
which contain few Symbiodinium, are retracted during the day and only extended at night for
feeding on active zooplankton."
I have yet to see anything regarding gas exchange and noctural axial corallite extension specifically in Acropora in my searches, I have only read of the axial corallite polyp extension being associated with feeding.