Let's say I have an app that can back up to iCloud Drive, like WhatsApp, on iPhone #1. I back it up to iCloud Drive. However, if I have the same app, WhatsApp, on iPhone #2 which is connected to the same iCloud account, will I be able to back it up to iCloud Drive as well, or will my #1 backup be overwritten?
The backup will be overwritten.
Your Apple ID is what's used to sync data between devices. It will take the most-recent change as what should be backed-up. iCloud will think that you want the most-recent change to be shared across devices and it will populate that change to all devices with that same Apple ID.
The way around this would be to use Dropbox or something similar as the backup. That way you can specify separate folders for the backup and prevent one from overwriting the other.