I presume 'not much' or 'you get an error', but I don't have an instance I'm prepared to sacrifice right now, just in case something hilariously destructive happens.
fsck doesn't run on a directory, it runs on a block device. You can't run it on /proc or /sys because those aren't backed by a block device. /proc only looks like it has a file system because the kernel "pulls" the "files" out of thin air when you try to access them.