I don't know about this. My first impression would be that Maesters and Septons would be accepted into the Watch as they are to take up a post suited to their already extensive training (medics, logistics, admin, spiritual well being, etc.). These types aren't expected to use a blade in anger (but then I haven't read all the books). But, I suppose if they had an Other bearing down on them they would swig for the bleechers.
If I were to make up a Septon for the Watch I would have be a little more of a Hawk, out spoken, then the rest of the Brotherhood, maybe train with a sword on the sly somewhere. Such a character, if found out, would probably be quietly "assigned" to the Wall.