Personally, I've found anything quota'd that is subsequently measured in the conjoint, such as 'current main brand' and also potentially sample source to be much more useful than segmentation covariates.
The quota bias partly accounts and controls for any differences due to oversampling particular groups (usually the client brand). Without 'current preference' sheer numbers of cases can 'infect' the smaller part of the sample. Any systematic quotas that are subsequently measured in the conjoint that don't 'naturally' fall out are candidates for this first bias.
Sample source is not always relevant, but it can help to offset systematic bias in sampling, which would be a hidden 'gotcha' if you don't look for it.
As I understand the relationship between HB and covariates, HBs strengths are that it can leverage population data to infer individual scores. Covariates strengths are that they can identify the correct population to infer from.