I'm not clear on the process or timing in a tank as some N is incorporated in algae tissue at least until its degraded.
In an algae farming operation or an algal turf scrubber application it seems harvesting would limit alk put back . So ,suppose there is no harvesting and no degradation? How does the N move to nitrate, When it's assimilated into tissue is there a reaction affecting alkainity I'm unaware of?
So for the reasons mentioned above, ammonia (not ammonium) conversion into tissue has no impact on alkalinity. Nitrate conversion does add alkalinity, exactly offsetting the loss in alkalinity when ammonia is converted into nitrate.

So a turf scrubber should have no impact on alkalinity, unless one is adding ammonium salts to feed it. If one is relying on fish waste, then that is essentially the algal growth process in exact reverse, so there can be no net gain or loss of alkalinity by going through the loop from algae (fish food) to fish waste and back.
