IME, no, there is no assumption such as that. Nor have I ever come across a standards organization which would specify any such assumptions. I have seen specific company standards that cover "typical conditions" for certain assembly/mating features, but they are very broad.
1) You're not going to press a standard dowel into a blind hole until it reaches hole depth. That's actually quite dangerous unless you also provide a vent hole or grind a slight flat on the dowel (among other solutions)
2) The actual important thing is the dowel projection length. Unless the fabricator knows the mating part, it is not safe to assume what the required projection is. It might be a very shallow pocket in a mating part, or it might be a bushing with a through hole.
3) I'm not sure why you would have a pin ever be pressed flush to the surface unless it was being used as a plug. I don't think most people would assume that a dowel pin gets pressed flush. That seems, IME (however limited my experience may be as one person) to be an exceptional case rather than a case to assume such a condition.
IMO, if you are setting specific requirements, you should show an as-assembled state with a dimension of the pin projection length and tolerance. If it is to be flush, that should be specified in the note, such as [PRESS FIT, FLUSH OR SLIGHTLY RECESSED .03" MAX, NO PROTRUSION ALLOWED]
(edits to fix horrible grammar on my part)
