There is a solution to what I am looking for. Copying email from Henry Oswald, ShareLaTeX co-founder:
The best option for what you want might be to publish the project as a
template (left hand menu) this will give you a web page with the pdf
you can give to the students. It will auto update each time you press
the publish button.
Regards Henry Oswald
When opening the template in ShareLaTeX, you just click on the image of the compiled document on the left side and copy the url it generates.
The only drawback to this is that by saving your document as a template, you make it publicly available to all ShareLaTeX users - but for now I am fine with that until I am through editing/revising. In ShareLaTeX, though, there is also an "Unpublish" option.
UPDATE: You need to know that in editing your document in ShareLateX, you have to "Republish" to the template, and then it will generate a new pdf which in turn gives a new url. So I am hoping someone will provide a solution with a STABLE URL so I do not have to update the link every time I revise my document!
UPDATE 2: Sharelatex.com no longer offers this (for free anyway). Currently using Papeeria which does exactly the trick (for free). But if you use this service you can only have one such 'public' document, which works fine for me since I'm writing a book and wanted students to have the latest edits.