Asking respondents about their purchase intent for partial-profile defined products is somewhat tenuous. I realize that ACA did this for decades, but I don't think it was ever argued that the purchase intent ratings for ACA's calibration concepts were accurate in an absolute sense for predicting real-world adoption rates. They were more used as a relative indication of purchase interest, as a way to try to scale ratings-based utilities to be more appropriate within choice simulators, and as a way to try to identify inconsistent vs. consistent respondents.
Regarding partial-profile and CBC with the None, the Patterson/Chrzan paper presented at our 2003 Sawtooth Software Conference showed that the None usage (for standard None) was affected by the number of attributes shown in the partial-profile display. I know that Dual-Response None is a little bit different animal, but I suspect the finding would generalize to the dual-response None.
So, in short, I'd proceed cautiously with trying to interpret the None when using Partial-Profile CBC. If you believe you are on reasonably firm ground, then you could turn the None "on" in our market simulator, so that a certain percent of respondents' "votes" in the simulator are assigned to the None category rather than to the other products you place in the simulator.
One does that by editing the Scenario, clicking the Advanced button, and setting the None weight to 1.0.