I doubt it. Most school software still sends files over e-mail that you have to save as attachments, or upload your own document files. So they still learn that early, regardless of if they use it later in life.
How does that work for most people? Are they organizing the files on a traditional file system or clicking on an icon in the message to open them or picking uploads from a selector which blends cloud and and app boundaries? Based on my wife’s school and the one our son attends, a LOT of the areas which used to expose file system behavior have been removed or significantly de-emphasized.
Not the case universally. My son's school in south-central UK does everything via Google Docs or apps specially built for distance learning. If it weren't for Minecraft mods, he'd have no concept of the file system.
Well, in Google Docs you have something that looks a lot like a hierarchical filesystem (whether someone actually creates folders or not). The fact that it's not actually a filesystem as traditionally understood is sort of irrelevant. The average filesystem user didn't know about inodes, journaling, etc. either.