Things have obviously changed since iOS6 then?
If you are using iCloud Photos, yes. There isn't enough information in the OPs statement to make a conclusive answer.
Things that should be included:
iOS Version
OSX Version (since he said photos I am assuming it is 10.10+)
Size of photo library (to the nearest .5 GB)
iCloud Drive storage size (free or paid plan at what tier)
As you had posted, the user will need to delete the photo from both their Mac and their Phone for the photo to be completely deleted if they are not using iCloud to store their photos.
As I assumed with 4000 photos they'd probably go for the iCloud Photos solution where they get backups, redundancy, the ability to have all of their photos on their phone without the need for much space, plus automated syncing of changes. It's honestly the best solution for large libraries, if the OP had < 500 photos then I'd say the old iTunes sync would be the better way to go. Cost to benefit.