I've done it both ways. Make sure to match your sample to your population (i.e. if you want to restrict predictions to those who said they might be interested, then project to that number using only those people in your simulator).
Now, if your respondents answered very well, you might hope that those who said they weren't interested also have very large utilities for none so that if you would include them in the simulator you might project to similar market size numbers as if you took them out and projected to the smaller universe size. Depending on how the none alternative was worded (and whether you had one and how respondents used it) this match between the projections might be better or worse.
I usually run it both ways, to see if they're different, and if they're different, I go with the one I trust more. On at least one occasion where I was torn between the projections, I simulated both ways and then used the average for my forecast.