This question relates to privacy, in that one may wish to not post material even after tentatively typing it into the edit box. Prior to clicking "Post Your Question", I notice there's often a "draft saved" message. Is any of the material viewable by anyone else at any time if I decide not to post it?
No, the drafts (we only support one per question, one per answer, per user) are not visible to anyone but you.
They are saved on the server so as Bill pointed out, you can see a draft across multiple machines.