Larry Solum gives advice to graduate students on the Legal Theory Blog about making unpublished work available on SSRN. He says in part:
"SSRN provides an electronic alternative to the former practice of making dissertations "available" via a service that will provide bound photocopies. I can't really see any downside to this method of distributing research. Of course, many dissertations will become books, and others a series of articles, but that process frequently takes years to complete."
I agree that SSRN is a great way to distribute unpublished work. Whether it is wise for a historian to make their dissertation, especially the entire dissertation, available on the web prior to publication is another matter. There are two things to consider.
First, if you're planning to look for a book publisher, if your manuscript is readily available on the web, publishers may think that web access will undercut sales. If a market for the book is for course adoption, students might just download the SSRN version, rather than purchase the book. With publishers concerned about making ends meet, and since academic books tend not to have large sales as it is, putting the entire dissertation on the web might undermine your chances of finding a publisher.
The second issue is more complicated. If your dissertation is based on painstaking original research, you may want the world to know about it now, and you can do that quickly by posting on SSRN. But then you run the risk that someone else might publish a book or article based on your findings before your own book or articles are in print. This can happen without anyone engaging in plagiarism or unethical conduct. All they need to do is appropriately cite to and quote from your work.
With very original research, the better strategy might be to get an article out as quickly as you can that includes the most important findings. That article (or at least its abstract) can be posted on SSRN, and the published article is then out there for others to draw upon. You can then reserve the remaining material for the book. The originality of the material, and the fact that others haven't used those sources, helps you attract book publishers.
It's hard to protect against inappropriate borrowing, which of course does happen. But putting too much of your research on SSRN before publication enables others to make use of your material in an appropriate way, but that could dilute the originality of your book when it appears.
The way I've handled this issue: with Cold War Civil Rights, I first published an article, Desegregation as a Cold War Imperative. It was the article that caused me to decide to write the dissertation & book, rather than the other way around. The article made my research strategy accessible to others (through my citations), but at least I had a publication out first. Later I published just one story in the book as an article for the Journal of American History: Josephine Baker, Racial Protest and the Cold War. A version of the story appears as part of chapter two. And I published an article on the Little Rock Crisis, which served as the basis for chapter four. Some of the most dramatic material in the book appears in chapters five and six, on the 1960s. When writing those chapters, I was careful about where I circulated drafts. For example, when a colleague writing in a related area asked to see my JFK chapter, I sent it but specifically asked him not to discuss or cite to stories in the chapter that I wanted to appear for the first time in my book, rather than his. (This is getting into a different topic, but: sharing work is a good thing to do, but there are also times when it is ok to decline, especially with someone you don't know who is writing something similar to your dissertation/book.)
With my new book, also based on difficult, extensive archival research, I published an article, Working Toward Democracy: Thurgood Marshall and the Constitution of Kenya. The rest of the research has not been posted on SSRN and has only been circulated for the purpose of workshops. It will appear for the first time in the book.
So...yes, you should use SSRN, but with caution. Consider posting the introduction and table of contents (here is an example). And get at least one article published before the book, which helps build excitement about what's to come!