Can SQL use an index while creating another?
You can do 

CREATE TABLE T(A INT, B INT, C INT)

INSERT INTO T 
SELECT 1,1,1
FROM master..spt_values

GO

CREATE INDEX ix ON T(A);

GO

--This won't benefit from existing index as noncovering
CREATE INDEX ix ON T(A) INCLUDE (B) WITH(DROP_EXISTING = ON);

GO

--This can benefit from existing index
CREATE INDEX ix ON T(A)  WITH(DROP_EXISTING = ON);

GO

DROP TABLE T;


There is no particular advantage of doing so in the first case. 

Whilst the existing index provides the desired sort order it will not be used for this as it does not contain the newly added column B and so it would require a lookup back to the base table for each row. The plan shows a table scan and sort.



The use of DROP_EXISTING here could provide benefit if you were removing an included column though - as in the second DROP_EXISTING example (as the original index would both have the desired order and cover all columns).

The plan for this shows that the original index was read to create the replacement.