Yes, one can download an image, copy it to their GDrive, and then be assured the images will be accessible....
HOWEVER - doing so means a teacher needs to budget time in their class to talk about fair use, digital rights, and copyright protection. When you copy an image to you google drive, you need to make sure you have the rights to do so.
So there's a tradeoff for teachers here, where you can choose to save time or make sure the games continue to work years later. Each teacher can make their own choice about their priorities, but it's important to make sure that it's an informed choice. :)