The (or an) answer is "it depends". Starting with DMT crystals, little will dissolve - but if you add base to a solution of DMT salt some may remain as a microemulsion and be very hard to get out of the water. This depends on things like concentration and temperature.
DMT freebase will dissolve into water when it can get protonated. Pure water will contain ~10^-7 molar of protons through its natural dissociation. But carbon dioxide dissolves in water and increases the proton concentration through the formation and dissociation of carbonic acid. This means that in practice, given very pure DMT crystals (no base or NPS contamination) you might be able to see more than a trace of solubility.
When you talk about increasing the ionic strength bear in mind that it then ceases to be distilled water.
The point of adding salt is that it helps to push the effectively non-polar DMT out of solution at a molecular scale while it is being formed through addition of base to a solution of a DMT salt. It also reduces the solubility of the NPS that will be pulling the DMT out of the aqueous phase.
“There is a way of manipulating matter and energy so as to produce what modern scientists call 'a field of force'. The field acts on the observer and puts him in a privileged position vis-à-vis the universe. From this position he has access to the realities which are ordinarily hidden from us by time and space, matter and energy. This is what we call the Great Work."
― Jacques Bergier, quoting Fulcanelli