Backup crisis: Will Time Machine backup iCloud Drive files ? Will it backup Box?
By default, iCloud Drive files are backed up with Time Machine. You can find them in this folder:

/Users/username/Library/Mobile Documents/


where username is the username of your account.

Note that if you have excluded the the Mobile Documents folder, Library folder, etc. from Time Machine - then the files will ofcourse not be backed up.

Also note that Time Machine can only backup the files that are actually on your computer. If you have set iCloud Drive to optimize storage usage, some files could be stored only in the cloud and not on your own computer. You can see that in the Finder when opening the iCloud Drive - a cloud icon will appear to the right of those files that are not stored on your computer. They will then not be included in your Time Machine backup.

The same applies for files on Box.com and other cloud storage service. If the files have indeed been stored on your computer, and you haven't manually excluded them from the backup, then they're included in your Time Machine backups.