Fyrffytr1, the answer to your question is, "Apparently, just a very small possibility." There is ongoing debate among the experts on 20th Century US Army buttons about when the "Great Seal" buttons first started being made with "black finish" on them. I said a "very small" possibility that it is from 1910-to-1917 because the US Army was very small during that period in comparison to its huge size later on, so not nearly as many US Army buttons were made for it as were made for it during the run-up to (and through) World War 2, when multi-millions were manufactured. I'm just pointing out that the vast difference in the production quantity from 1910-1916 and the WW2 era indicate it is far-far more likely that GA-digger's non-black-finish rimmed Great Seal button was manufactured in the World War 2 era than in 1910-1916. Kinda like the odds greatly favor a plain-shield "eagle button" being made during 1861-1865 than made during 1854-1860. Rockermike17368 is TreasureNet's resident expert on 1902-to-present "Great Seal" US Army buttons.
http://www.treasurenet.com/forums/what/112828-great-seal-button-backmarks-help-5.html He says he is working on a book about them. Perhaps it will answer our questions about 1910-1916 ones.