Especially with the sun coral polyps the phyto will not sustain them. They need some kind of meaty food such as mysis. For the most part, lps corals that people typically feed should be fed meaty foods. They also feed of DOM (dissolved organic matter) but these are nutrients so to speak so you don't want too much (a protein skimmer pulls this stuff out). So yes, feeding corals can make your nutrient levels rise as well. Unless you have filter feeders (feather dusters, sea squirts, etc) I'd hold off on the phyto. Good luck with the sun polyps.
Good on ya
Aaron