of course you can have a tank without substrate. it will make cleanup easy and will, to a degree, aid in prevention of certain diseases and anaerobic bacterial growth. be aware that a bare-bottom tank will show every single solitary little speck of dirt and detritus on its smooth glassy surface. substrate will often hide such imperfections (but of course, will also harbor the sludgy grossness).
however, any natural aquatic environment has a substrate; a place for beneficial bacteria to grow, a place for certain fish to burrow, a place to absorb light (which, when too bright, can make many fish uncomfortable), and a place from which plants can grow(almost all species of fish will be much healthier in a planted aquarium).
so naturally, there are certain advantages to a bare-bottom tank, but often such advantages are better suited to a quarantine and/or hospital tank.
so the short answer is yes, you can easily maintain a happy, healthy system without substrate. but the benefits of substrate are numerous and should be considered in your decision.