I can find research that indicates sodium nitrite was used to feed the NOB. However, lab research and actual practical application in hobbyists tanks are two different issues.
I see a few potential issues which may or may not be relevant in answering this question. The first is that higer levels of ammonia and/or nitrite have an inhibitory effect of the nitrifying bacteria. In a normal cycle the ammonia oxidizers become pretty well established before the nitrite levels rise. This would suggest that ammonia levels are under control by the time nitrite levels build. It might be possible that dosing both ammonia and nitrite at the outset would create overall conditions unfavorable for the development of either or both ammonia and nitrite oxidizes.
Further, salt can act to inhibit the nitrogen cycle on fw systems once salt levels rise beyond a certain level. What happens to the sodium part of the sodium nitrite?
Further, sodium nitrite is used as to kill certain bacteria. While this effect is normally related to gram negative bacteria and the nitrifiers are gram positive, this does not mean there are not other desired bacteria in tanks which could be negatively effected by nitrite in this form.
Given all the issues relating to the use of ammonia to cycle, I wonder what this would mean for sodium nitrite. Where would one buy it in a known concentration. Given how many problems new fish keepers encounter trying to dose ammonia, how many more things could go wrong by complicating this with another chemical to dose and test.
And how would one control overall nitrite levels. One would be dosing nitrite on one hand and the ammonia oxidizers would begin to pump out nitrite. The normal relationship between the AOB and the NOB would no longer be a natural one since we would be upsetting the balance by adding nitrite. This whole thing would be complicated by the differential rates of reproduction for the two different types of bacteria.
In the end, I think it becomes much simpler and less uncertain to use either seed material from established tanks or a bacterial additive such as Safe Start or One and Only.
However, from a more tightly controlled scientific point of view, the proposition makes sense. One question does occur to me- why choose sodium nitrite as opposed to potassium nitrite?