Ok I was wrong
Sorry to sound like a jerk but I had never heard of this practice and it seemed so unusual that people would actually dose nitrates into a system when so many people work to minimize them. At the very least you run the risk of nuisance algae blooms and other problems. However in the case where you have little nitrate being actively generated in your system (for example a fish-less system where you are not adding any food) I could certainly see a long-term absence of nitrates having a negative effect on not only clams, but on any other invert that relies on symbiotic algae for a large portion of its energy.
After researching this subject a little more thoroughly, I have found additional references of clam farms in Palau and the Solomon Islands that use solutions of dillute ammonium nitrate to provide additional fertilizer for clam growth. It should be noted that you are fertilizing the algae itself within the clam, not really feeding the clams directly.
From the Center for Tropical and Subtropical Aquaculture, Publication #130,
Spawning and Early Larval Rearing of Giant Clams (Bivalvia: Tridacnidae) by Simon Ellis:
A daily addition of 100 mM ammonium nitrate (4 g per 1000 L of tank volume) in the morning is sufficient to raise nitrogen levels for the rest of the day. Note that this is used in semi-closed systems in land-based farms, which is probably most applicable to our reef setups. Also note that this use of fertilizer was accompanied by
use of herbivorous animals such as rabbit fish, surgeon fish or Trochus, in combination with regular cleaning to prevent excessive algal fouling in the tanks which I would guess would be a problem in a fertilized environment with bright lighting.
Hope this helps
I always wondered when I dosed my clams with phyto whether the clams were reacting positively to the phyto itself, or some of the dissolved nutrients in the phyto culture media. Interestingly, it is one of the explanations given for why NOT to try to feed larval clownfish with phyto (or try to maintain high phyto cultures in larval fish systems): the nitrate levels are too high and have a negative impact on larval health.