Does Index Intersection work with Included Columns?
Included columns don't prevent the index being used for any purpose. 

The query optimizer will pick the best index (or possibly a table scan) that is the most efficient for the query being compiled.  Keep indexes as small as possible, while still providing the desired functionality.  According to Books Online INCLUDEd columns don't affect the query optimizer's selection of an index based strictly on size, however if any given index has all columns required for a query, either as key columns or included columns, that index will be given priority.

Since the query optimizer is a fairly opaque beast, you most likely need to test the suggested index to see if it is used, and what the resulting impact is for INSERTs, UPDATEs, and DELETEs.