Many bishops, in fact most, will take advantage of this streamlined process, especially since Francis has basically told them to not impose any fees for annulments. He didn't go as far as I wanted, but he went pretty far, and effectively endorsed the American norms for annulments. He's just shortening the time, which was a major stumbling block for lots of remarried Catholics and those wanting to become Catholic.
The truth of the matter is that many priests already take care of the Communion question in the internal forum of confession. In other words, Catholics who feel they have a case but don't want to go through the long annulment process go to confession and the priest tells them to just go ahead and receive the Eucharist. Like it or not, this happens, a lot.
And many Catholics who have remarried without an annulment just decide on their own to go, especially if they've been told they have no grounds for an annulment.
On the other hand, many many Catholics have left the Church over this issue and will never return, since they've made peace with God outside the strictures of Catholicism.