Yes scrubbers reduce nitrates; and nitrite, phosphate, ammonia, and CO2. Algae is the natural filter of all oceans and lakes. Also the natural food producer.
The Smithsonian tank is a closed ecosystem experiment; the pics I saw many years ago, at that time, had already gone 8 years with no intervention. The goal was/is to see how water parameters are kept in check, and they stayed better than parameters of real reefs. As for public aquariums:
Great Barrier Reef Aquarium
Many people say how the Great Barrier Reef aquarium (or other public tanks) was a scrubber "failure" because the corals did poorly. Apparently these people have not done much reading. In the early days of that aquarium, the scrubber was doing it's job great:
1988:
Nutrient Cycling In The Great Barrier Reef Aquarium
http://www.reefbase.org/download/download.aspx?type=10&docid=10506
"The Reef Tank represents the first application of algal scrubber technology to large volume aquarium systems. Aquaria using conventional water purification methods (e.g. bacterial filters) generally have nutrient levels in parts per million, while algal scrubbers have maintained parts per billion concentrations [much lower], despite heavy biological loading in the Reef Tank. The success of the algal scrubbers in maintaining suitable water quality for a coral reef was demonstrated in the observed spawning of scleractinian corals and many other tank inhabitants."
But, did you know that they did not add calcium? That's right, in 1988 they did not know that calcium needed to be added to a reef tank. Even five years after that, the Pittsburgh Zoo was just starting to test a "mesocosm" scrubber reef tank to see if calcium levels would drop:
1993:
An Introduction to the Biogeochemical Cycling of Calcium and Substitutive Strontium in Living Coral Reef Mesocosms
http://onlinelibrary.wiley.com/doi/10.1002/zoo.1430120505/abstract
"It was hypothesized that Ca2+ and the substitutive elements Sr2+ and Mg2+ might [!] have reduced concentrations in a coral reef microcosm due to continuous reuse of the same seawater as a consequence of the recycling process inherent in the coral reef mesocosm."
"The scleractinians (Montastrea, Madracis, Porites, Diploria, and Acropora) and calcareous alga (Halimeda and others) present in the coral reef mesocosm are the most likely organisms responsible for the significant reduction in concentration of the Ca2+ and Sr2+ cations."
"Ca is not normally a biolimiting element [in the ocean!], and strontium is never a biolimiting element; HCO3 [alk] can be. It appears that, because of a minor [!] limitation in the design parameters of the mesocosm, these elements and compounds may have become limiting factors. [...] It is surprising that the organisms could deplete the thousands of gallons of seawater (three to six thousand) of these elements even within two or more years [!!].
"The calcification processes are little understood."
So then, in the late 90's, the Barrier Reef aquarium start using up it's supply of calcium, and the folks there said "the corals grew poorly". Really. No calcium, and the corals grew poorly. So they "removed the scrubbers" and "experimented with the addition of calcium" sometime after 1998. Then in 2004 it "definitely improved a lot". Really.
Talks about calcium was not added to the Barrier aquarium:
http://en.microcosmaquariumexplorer.com/wiki/Reef_HQ_-_Great_Barrier_Reef_Aquarium