If you add columns without populating them, then it is pretty quick as it is just a metadata change. Adding an index does require the table to be read (or potentially another index) so that can be very time consuming and of much greater impact than the simple metadata change of recording the new index details.
If the new columns are going to be populated as part of the ALTER TABLE, it is a different matter.
- The database may undergo an unplanned shutdown during the course of adding that data to every row of the table data
- The server memory may not have room to record every row changed in that table
- Therefore those row changes may be written to datafiles before commit, and are therefore written as dirty blocks
- The next read of those blocks, after the ALTER table has successfully completed will do a delayed block cleanout (ie record the fact that the change has been committed)
If you add the columns (with data) first, then the create index will (probably) read the table and do the added work of the delayed block cleanout.
If you create the index first then add the columns, the create index may be faster but the delayed block cleanout won't happen and that housekeeping will be picked up by the application later (potentially by the select * from T where C = whatever)