You are correct on the selecting an index as a 'candidate index' to be used. Only the index key values are used. However, after an candidate index is identified, the included columns are used to determine if it is a covering index or not. If it is determined that it is a covering index than that index will be used in the execution of the query.

The question then becomes does SQL treat the selection of covering indexes the same way it does the selection of candidate indexes. left to right and stopping at the first mismatch or does it just look for all the columns required before determining if it is a covering index.