Auto-organization is optional. You could just select tracks, and apply a naming template manually (File> Organize Files). If this is first time, you'd better start testing with a small sample of files to learn how the template works, without using auto-organization option. The benefit of auto-organization is whenever you change a tag or import a new track, they auto-move to a new folder. Otherwise, it's the same as using templates manually.
I'm not sure how BTsync deals with moved files. I'd just apply the template to each machine manually, and then turn it on again.