The short answer is: “No.” Time Machine only backs up files that are stored locally on your computer.
But a longer answer is more complicated.
Time Machine is a built-in feature of the macOS that automatically backs up personal data, including apps, music, photos, email and documents. You can use it in case you accidentally delete the wrong file, or need to restore your files to a new Mac.
Time Machine uses an external storage device connected via USB or Thunderbolt. This storage device needs to be dedicated to Time Machine, you can’t use it to store other files.
NOTE: While you can use Time Machine with only one drive attached to your computer, it is best to use it with external storage. That way, if your computer dies, all your personal data is safe.
Ideally, Apple Help notes, “your backup disk should have at least twice the storage capacity of every disk or volume you’re backing up. If your backup disk doesn’t have enough storage space to contain a complete backup, Time Machine will let you know.”
NOTE: Here’s the Apple Support page that explains how Time Machine works.
By default, recent files that are stored in iCloud are also stored locally on your system. Those files will be backed up by Time Machine. Files stored outside the Desktop or Documents folder are not automatically transferred to iCloud.
WHAT DOES STORING FILES ON iCLOUD DO?
Apple Help says: “When you sign in to iCloud, you have access to iCloud Drive. You can store files in iCloud Drive as long as they’re 50GB or less in size and you don’t exceed your iCloud storage limit. If you need more iCloud storage, you can upgrade to iCloud+. With iCloud+, you can also share iCloud storage with your family, without sharing your files.
NOTE: Apple recommends that you “avoid storing app folders, libraries, .tmp, .vmdk, .vmware, .vbox, .vm, and .pvm files in iCloud Drive.”
iCloud files are automatically backed up by Apple. If you need to recover a deleted file that was stored on iCloud:
WHAT DOES THE OPTIMIZE STORAGE SPACE SETTING DO?
One of the system storage settings is System Settings > Storage > Optimize Storage Space. Apple Help says: “When space is needed, you can keep files, photos and videos, Apple TV movies and shows, and email attachments in iCloud, which makes them available on demand. Files don’t take up space on your Mac, and you can download the original files when you need them. Recent files and optimized versions of your photos are always on your Mac.”
SUMMARY
So, back to the short answer. If you store files locally, Time Machine will back them up. If not, not.
