I don't use Google Drive myself, so I can't comment on what they offer, or if this includes public image hosting.
What I can say is that the Machine Learning for Kids web server is able to access images that are publicly accessible on the Internet.
It cannot use your Google account credentials to access your private images.
Put another way, if I could access your images in your Google Drive, there is a reasonable chance that the Machine Learning for Kids server can. If I can't access your images, then my web server won't be able to, either.
The training data limit for an images project stored on the Machine Learning for Kids server is 100 images.
There is no training data limit for images project that you store on your own computer.
Kind regards
D