Do files take up space on my laptop?

Currently using Adobe Creative Cloud Teams for work (design agency, 10+ employees) but we're looking into Enterprise as a storage solutions (want to replace our exisiting server which is dying and move completely cloud based instead).

I have a question about storage - currently our Indesign files are saved locally and synced to the cloud, but these are taking up space on our laptops. Once we move our entire server over we will run out of space on our laptops (which defeats the object of cloud storage in the first place).

I assumed CC was similar to Google Drive and didn't take up space locally but it seems that isn't the case?

Turning syncing off isn't really an option as the way we work in Indesign uses live files with live links, so downloading/packaging isn't an option.

Is there any way to stop CC syncing certain files? (like Dropbox does), or are the inly options sync everything or sync nothing?