No. Time Machine requires a LOCAL external drive.
None of the cloud storage systems (iCloud; DropBox; G-Drive; OneDrive, etc) should be used for full backups. Their speed is limited to that of your internet connection. Moving 100s of gig of information can take too long, and risk of date loss if the internet winks out on you for a few seconds.
How many USB devices are connected to your Mac?
You can try "waking up the Passport."
— If it has nothing on it, use Disk Utility to erase and reformat it. Set the partition scheme to GUID Partition Map: and the file system to APFS. Getting rid of the odd partition and formatting scheme Passport ship with often helps with the low power issue.
You can put a POWERED USB hub between the Passport and the computer to get the external more power. Powered means the hub has its own power supply.