Can I back my Macbook up to iCloud Drive using Time Machine?

No.

Excerpted from Backup disks you can use with Time Machine - Apple Support:

To use Time Machine to make a backup of your Mac, you need one of these types of storage devices:

• External USB, Thunderbolt, or FireWire drive connected to your Mac
• Network-attached storage (NAS) device that supports Time Machine over SMB
• Mac shared as a Time Machine backup destination
• External drive connected to an AirPort Extreme Base Station (802.11ac) or AirPort Time Capsule
• AirPort Time Capsule

iCloud Drive mirrors what's on your drive. At least the parts you allow to be put on iCloud Drive.

If you have the space, you can copy any amount of data to a folder on iCloud Drive. But a lot would be duplicated.

iCloud Drive is an interactive service and responds to deletions and additions on your local drive. It's not designed to be autonomous long term cloud storage.

Time Machine is at its best when used as designed: a dedicated backup to a local external drive.