You raise a very interesting question--one that is also quite specific. Though I haven't fully researched the history of Sabbath School in the Adventist Church, I can still say with a fair amount of confidence that it was not "divinely inspired." Neither was "the worship hour," however. The early Adventist worship service was patterned after other Protestant denominations for the most part. In fact, during the earliest years of Sabbath School, SDA's had to rely on published sources made for Sunday Schools so that they could have material from which they could teach. Naturally, they altered the theology to fit Adventist beliefs first.
Both Sabbath School and the worship hour have evolved greatly in the Adventist Church throughout the years. For example, it was strongly recommended (and practiced for years) that Sabbath School classes should be limited to 3 or 4 members plus one instructor. In May 1863, George W. Amadon (one of the pioneers of the Sabbath School work) stated in the Youth's Instructor (p. 37-38), "These [i.e., the Sabbath School classes] should not be too large. Four is a great plenty for a class, and two or three will often be better than more. By having the classes small, a greater number of teachers will be brought in to the work, and the scholars also will regard what the teacher says as applying more directly to them." (emphasis is in the original). In other words, early Adventists believed it important that Sabbath School classes be small--very small, actually--so that more people could be involved in teaching/leading and the students would feel personally accountable and take the class seriously. (It is also interesting to note that Battle Creek followed this policy for 2 or 3 decades, even after church membership was quite high. I have seen as many as 78 different classes in that church, if memory serves me correctly, in the late 1870s or early 1880s. Can you imagine that today?).
This is just one example, but I think it is relevant. You wished to know: "Was the Sabbath as we know it today divinely inspired." Since Sabbath School classes are not limited to 2, 3, or 4 members, the answer seems to be "no." In other words, we don't carry out Sabbath School in the same manner as Ellen White or her contemporaries, so even if she did suggest that Sabbath School was "divinely inspired" (and I am quite certain that she never did), it would be absolutely crucial to put her statements within the proper historical context. Please understand that I am not suggesting that the way we do Sabbath School today is off the mark, or even a deviation from Ellen White's counsel. It is simply different. It is an abuse of history to suggest that the present should look exactly like the past, even in regard to the way we do our church services.
I hope that my response has been helpful to you in some way. I will suggest a few more things that can help you dig deep if you so desire.
1. Visit egwwritings.org to explore all of Ellen White's writings. You can search for the phrase "Sabbath School" (in quotation marks) to see everything she ever wrote on that topic.
2. Visit adventistarchives.org to explore some of the early issues of the Youth's Instructor. Reading through the early issues of this paper will give you an good idea of what Sabbath School used to be like in the Adventist Church.
3. Visit the Center for Adventist Research in person and check out some of the following books: General Conference of Seventh-day Adventists, The Sabbath School: Its History, Organization, and Objectives (Washington: Review and Herald, 1938); L. Flora Plummer, Early History of the Seventh-day Adventist Sabbath-School Work (Washington: Review and Herald, [1911?]).
4. I do not know of any dissertation that addresses the topic of Sabbath School. I do hope to write a history of the local church one day, but whether or not that will happen is up to the Lord.