My assumption is that the index will not be dropped .. You should be able to continue using the table and index when the reorg is happening if you specify ALLOW WRITE ACCESS ..
The reorg is generally done in the tempspace or another tablespace you specify and then the original index is 'swapped' for the new one ... Even if you specify ALLOW WRITE ACCESS there will be a short period of time when the index will not be available .. By default, The INPLACE reorg is different and happens asynchronousely ..
But, the bottomline, to my understanding is, the index is not dropped
HTH
Sathyaram