Necessary to have separate index for lookups against one of a multi-column PK?
In short, it is sufficient. As far as the searched field is the first in a composite index (PK, unique, or regular index), no need for other separate index.  

However, you mentioned that you 


  (won't be using an autoincrement column)


Is there a reason for that? Composite PK might have performance hit, specially if you are using InnoDB engine, and if you have many updates on the table (insert/update/delete)