What do you deem "insignificant"? The required daily dose is about 90 mg. There are experiments which include several grams [1, 2, 3], which is a large enough dose that those writing the papers call it a "megadose". If you consider a megadose to be 1,000g and 10,000g, then I think that's just moving the goal posts. Is there a dosage level at which you would say, "Yes, with no clear signal at that level, it's probable it makes no difference"?

[1] http://www.ncbi.nlm.nih.gov/pubmed/11700812?dopt=Abstract

[2] http://www.ncbi.nlm.nih.gov/pubmed/23440782

[3] http://www.ncbi.nlm.nih.gov/pubmed/8191227, shows some positive evidence, which may be noise, and concludes "needs more research" - despite there already being a lot, with no clear positive signal.