They traded for Garland 4 years before Cooper took over as pitching coach. Mark Buehrle was drafted in the 38th round, also 4 years before Cooper took over. They both greatly succeeded under Cooper though.
Ignoring Quintana, (I'm not going to define that a minor league free agent was acquired as major help), the last person acquired via trade or free agency on that list was Jake Peavy 9 years ago. So yeah, I think that adds to the point.