Algae do not store nitrogen that can be accessed for further growth. However, it does bind nitrogen in its biomass that can be released when it decays. I think actually releases organic carbon as part of the photosynthesis process rather than storing it. It needs a source of nitrogen... but that does not mean it has to be nitrate. Ammonia would be used first.There are a variety or resources to look at. Just randomly choosing this one states that algae growth is limited by the availability of nitrate and phosphate. So they need nutrients in the water column not storing them for a rainy day. Algae can store energy and stuff like carbs but not primary nutrients from the sites I have looked at.
Nutrients and Eutrophication | U.S. Geological Survey
Like people, plants need nutrients, but too much of a good thing can be a problem. Nutrients, such as nitrogen and phosphorus, occur naturally, but most of the nutrients in our waterways come from human activities and sources—fertilizers, wastewater, automobile exhaust, animal waste. The USGS...www.usgs.gov
What are Phytoplankton?
Microscopic plant-like organisms called phytoplankton are the base of the marine food web, and they play a key role in removing carbon dioxide from the air.earthobservatory.nasa.gov