dm_db_missing_index_details - does the order of equality_columns matter
In this case the single index you propose could be used to satisfy all three equality searches.  If any of the columns allows null values, it may matter which order the columns are in.  

The optimizer should match the index regardless of the order in the query.  What is important that the equality conditions match the leading columns in the index.  The proposed index would not be good for an equality condition on client_id or stats but not including client_product_id.

In some cases the index may be used if the first field is referenced, but one of the subsequent values is skipped.  Depending on data distribution an optimizer may use a range scan on the proposed index to search for equality on client_product_id and status but not client_id.