Will my devices still sync when switched off?
No. Resilio Sync is not a cloud storage solution like SkyDrive/DropBox/GDrive, etc - is moves data directly from one of your devices to another. Since there is no "cloud" involved, the source device must be online for syncing to work.
If you require an always-on "cloud" functionality for Sync, you can run Sync on a number of commercially available Network Attached Storage (NAS) devices, or you can check out companies now offering dedicated Resilio Sync solutions, some of which you'll find listed here.