Yup that's trivially easy if you have permissions to use mknod and mount. (and if the file system namespace looks like it normally does all you need is mount.)

Docker is for organizing things for yourself, just like directories are. If you want actual isolation you have to take extra steps.

EDIT: and I feel like I should add those extra steps are exactly what most server software does automatically when it chroots itself. Again docker is really just for organizing things.