Hello,
I would say yes, however, that would depend on a few things.
1. How many fish, how often fed?
2. How large water changes with what frequency changed?
3. Are you running any kind of mechanical, chemical, or biological filtration? (eg. fuge)
Simple rule of thumb with sps is keeping the alk stable. Also, keeping pristine water, where regular feedings to a heavier fish population is what sps seem to thrive in, at least for coloration. So, whatever goes in, must come out, that is why most sps keepers tend to not only run a skimmer, but usually one that is over rated for the system requirements. Can this be done, yes, but you will likely being doing a couple large water changes per week, so find a salt that dials you in to the parameters you prefer, at least for alk. Red Sea makes a good salt, lower in alk, I prefer this for example because I prefer lower alk. That said, I do not have to worry about water changes altering my desired levels, I sort of maintain my alk at the same level of the newly made saltwater to avoid any fluctuations, this is key for sps as I am sure you know. I would look up Arverly 20 gallon skimmerless on the Orlando forum, he seems to be doing well at the moment, but again.... What goes in must come out, so I personally would not do this, but it can be done, just seems like a lot of work, FWIW...
Cheers!!!