sql server – Will index on a partition that doesn’t include partition column work fast?

Let’s say I have a huge table with columns (CloseOfBusinessDate), (DataSourceID), etc.

(CloseOfBusinessDate) is a partition column and I have a clustered index on that column (on CloseOfBusinessDatePartition).

If I add an index on the (DataSourceID) column on the CloseOfBusinessDatePartition, will the following query work fast:

SELECT 
  * 
FROM
  MyTable
WHERE
  CloseOfBusinessDate = @cobDate 
  AND DataSourceID    = @dataSourceID

I.e., I expect SQL Server to quickly find the right partition and then use the index on the DataSourceID column for the fastest results. Am I right?