It's possible, I have a 12g mr aqua running for about 6 months. I have 20 or so sps frags in it and have only lost 3. One when i overdosed aminos and had a semi crash while away for a weekend and two when I recently moved. Weekly water changes are needed and growth is really slow but they can survive and I got really great color out of my pink sand dollar. Also I didn't have a heater in it for about 5 of those months. Not saying this is a good way to keep sps but it's possible with a wide variety in my experience. You do run into the issues of any small change is potential disaster tho.
I have know someone who kept some acros in a 1g fish bowl last summer as an experiment. 50 percent wc every day, sometimes twice, with no circulation on a roof top in direct sun. They grew over an inch but I assume were not happy.
I would recommend a skimmer/hob filter, no fish or only a goby and some kind of flow and a heater, walmart has a 50w about 6". For corals I have seen the purple with green polyp (gar bonsi, valid tricolor types) maintain color and growth as well as red planet and pink sand dollar in my experience.