I suspect that if you keep the same BR name and overwrite the existing one as you say then the updated business rule will apply to all the flights that you have this rule assigned to and will reflect your changes
If you changed the BR today then tomorrow morning when the inventory controller runs it will update all the AU's on the flights that have that business rule assigned to them to reflect the new structure
So long as the business rule number does not change after they re-save the BR it should be fine. BR's are assigned to flights using this number.