If my understanding of the chemistry involved is correct then inorgainic sodium bromide will eventually form bromates (which do not 'reactivate' into hypobromous acid) and then you will have a chorine pool again. It is the organic form of bromine found in bromime tabs that contain dimethylhydaytoin that sticks around forever.
Ben (PoolDoc) summed it up on this PoolSolutions page
http://www.poolsolutions.com/tips/tip10.html

Hope this helps.