I've done this a couple of different ways.
The first is as you suggest - run the simulation, identify the folks who would likely buy your target product and then take that data out and run some predictive modeling to see which other variables (demographics, psychographics, etc.) are significantly related. You can do this via correlation analysis or ANOVA, but if your number of potential predictors is large, I'll often run a discriminant analysis or a classification tree to find the significant predictors.
The second is one we don't do all the time, but that works nicely when you can anticipate the need in advance. Here we have all the potential profiling or predictor variables also loaded into the simulator and we build a custom Excel simulator. In addition to showing the shares of each product you've configured in the simulator, it also shows summary statistics for each (demographic/attitudinal/behavioral) predictor for which you have data. We often call this a "profiling simulator." It's enough of an effort that we don't do it all that often, but, as you can imagine, when it's the right tool for the job, it's really nice to have!