Well if they sign tomorrow, they wiil have to get their building permit from the local bishop.
http://www.richmonddiocese.org/A Message from Bishop DiLorenzo
Welcome to the Diocese of Richmond. We hope you’ll find our website a reflection of who we are as a diocese and our commitment to Word, Worship, Community and Service.
The Diocese encompasses over 33,000 square miles of the southern part of Virginia. Founded in 1820, we are one of the oldest dioceses in the country, with 147 parishes stretching from the Chesapeake Bay and Atlantic Ocean west to West Virginia and Tennessee. Ours is an active and vibrant diocese, committed to supporting cultural diversity, marked by a spirit of enthusiasm for mission and ministry.
Relations of the Society of Saint Pius X with diocesan bishops
DICI: A personal prelature is the canonical structure that you mentioned in recent statements. Now, in the Code of Canon Law, canon 297 requires not only informing diocesan bishops but obtaining their permission in order to found a work on their territory. Although it is clear that any canonical recognition will preserve our apostolate in its present state, are you inclined to accept the eventuality that future works may be possible only with the permission of the bishop in dioceses where the Society of Saint Pius X is not present today?
Bishop Fellay: There is a lot of confusion about this question, and it is caused mainly by a misunderstanding of the nature of a personal prelature, as well as by a misreading of the normal relation between the local ordinary and the prelature. Add to that the fact that the only example available today of a personal prelature is Opus Dei. However, and let us say this clearly, if a personal prelature were granted to us, our situation would not be the same. In order to understand better what would happen, we must reflect that our status would be much more similar to that of a military ordinariate, because we would have ordinary jurisdiction over the faithful. Thus we would be like a sort of diocese, the jurisdiction of which extends to all its faithful regardless of their territorial situation.
All the chapels, churches, priories, schools, and works of the Society and of the affiliated religious Congregations would be recognized with a real autonomy for their ministry.
It is still true—since it is Church law—that in order to open a new chapel or to found a work, it would be necessary to have the permission of the local ordinary. We have quite obviously reported to Rome how difficult our present situation was in the dioceses, and Rome is still working on it. Here or there, this difficulty will be real, but since when is life without difficulties?