will ALTER TABLE ADD COLUMN result in indexes being rebuild ?

 Rebuilding Indexes happens Rebuilding an index drops and re-creates the index.
And Modifies a table definition by altering, adding, or dropping columns and constraints, reassigning and rebuilding partitions, or disabling or enabling constraints and triggers. 

Indexes created as part of a constraint are dropped when the constraint is dropped. Indexes that were created with CREATE INDEX must be dropped with DROP INDEX. The ALTER INDEX statement can be used to rebuild an index part of a constraint definition; the constraint does not have to be dropped and added again with ALTER TABLE.
All indexes and constraints based on a column must be removed before the column can be removed.
When a constraint that created a clustered index is deleted, the data rows that were stored in the leaf level of the clustered index are stored in a nonclustered table. You can drop the clustered index and move the resulting table to another filegroup or partition scheme in a single transaction by specifying the MOVE TO option. The MOVE TO option has the following restrictions: