Without digging around in some chemistry books, I'm going to hazard an answer...
pH is influenced by the hydrogen ion activity relative to hydroxide ion activity they're oppositely charged. When it's hydrogen ion activity is high, a solution is acidic (low pH). When hydroxide ion activity is high, a solution is basic or alkaloid (high pH).
I don't think those ions are large enough to be measurable as solids in a TDS reading. Other charged particles (anions and cations), though, are large enough and can influence TDS. But pH can effect when certain chemicals dissolve or precipitate out of a liquid, so there is an effect.
Whether or not larger charged particles can influence pH, I'm not sure, but I don't think so.