No. The computers are on "deep freeze" which means that anything saved to them (desktop, C-drive, Documents, etc) will disappear once the machine is logged off. Unfortunately there is no way to get the item back if this happens. Ideally, you should save items to your OneDrive, Google Drive, or a flash drive. See the link below for more info and the instruction flyer on OneDrive.
If you can't use either of those, you could save something to the desktop then email it to yourself to have a copy.
