It is possible to use linear (continuous) variables within our LC software. For example, you can ask our LC system to model the Price or Speed attribute as a single coefficient, rather than using part-worth specification.
That said, Latent Gold does have more options for including non-conjoint variables within the run. So, you may want to do it for that reason.
One of my favorite ways to use latent class is just as a segmentation tool, and for the purposes of placing people into segments. You can then take those segmentation assignments, and merge those segmentation variables into our conjoint simulators (either the Online Simulator or SMRT) and use them as banner points and filters. The underlying utilities you are using for predicting peoples' choices are still HB utilities, but the segments are broken out by those discovered using LC.
Generally, I think it's better to ask LC to develop segments not based upon HB utilities (I believe Latent Gold can do that, as it can run Latent Class on a series of basis variables, similar to the idea of running cluster on a bunch of basis variables), but on the original DCM data: the design and the choices. HB involves some smoothing of the sample toward the upper-level model (often, the population). So, to try to develop segments based on variables that have already been involved in smoothing out differences between people and segments seems like going one step forwards and two steps back.
But, please talk to the Latent Gold people about that, as LC is their emphasis.