I have to wonder whether this Synod would be considered part of the Ordinary Magisterium.
I don't think I'm falling into error, even based on EWTN's definition. A synod does not fall into the definition. 1) It is not an ecumenical council; 2) it is not an ex cathedra statement of the pope; and 3) it could conceivably teach something at odds with the "perennial teaching of the Pope and the Bishops in union with him around the world", and therefore would not form part of the ordinary magisterium.
I did not mean to imply that that the Ordinary Magisterium is not infallible. Rather, I mean that synods do not necessarily form part of the ordinary magisterium any more than a bishops' conference does. The proof is in the pudding. If it agrees with the perennial teaching of the bishops in union with the pope, then it is infallible. If it does not agree, then it is not infallible.
And in any case, there is no guarantee that the Holy Spirit will prevent them from making a really bad decision on how to handle annulments.
That seems backwards thinking to me. Either a synod should be infallible or not. Either it is protected by the Holy Spirit or it is not. If it should be and the teachings contradict prior teaching, then we have a serious problem on our hands. In my mind, that would just be more of the same ala Vatican II.