Jim,
if you commence the MAP before the MAPt then clearly you must continue the azimuth guidance to the MAPt before commencing any turns. This is not news though, and is equally applicable to an ILS with a MAP before DA.
Yes, there are MAPts beyond the threshold - many non-DME approaches will have the MAPt at the navaid - NDB or VOR - which may well be somewhere on the aerodrome.