This is a good and also challenging question. If the purpose of running latent class were only to improve the accuracy of market simulator predictions (compared to an aggregate MNL solution), then the answer would be to include the None tasks in the latent class estimation and to use a large number of classes (say, 12+).
However, I suspect that the purpose of your latent class analysis isn't to improve market simulation predictions, but rather just to detect market segments for strategic segmentation purposes. If that's the case, then it's hard to say which latent class segmentation would be more useful to you (one that included the None parameter or one that ignored the None information).
You can get a sense of how much the None parameter is influencing your latent class segmentation result by comparing the utility of the None across your latent class segments. If the None utility is about the same, then you would think that it isn't driving the latent class results much.