Probably not going to happen. The Mormon troops would leave.
QFT...they are the power behind the throne in both numbers and $$$. While it's possible the BSA could take the the position described in the article where it becomes a local unit option, based on chartering organization guidance, I'd say the LDS-sponsored units would simply drop their BSA affiliation. This would shortly be followed by an LDS-only group similar to the Pentecostal Royal Rangers youth group.
This would essentially collapse the BSA as a national organization, along with its premier events (Jamboree) and High Adventure Bases (Philmont, et al). If there is any discussion going on among the board, it had better be around these types of issues and the potential for the LDS to take the road I described above.
The Mormon troops would leave.