Eh, not necessarily. Class consciousness is important, but thinking that it completely overlaps with social consciousness not true. People compartmentalize things.

For example male black homophobes are common in America; Which is ironic because one would think that a black male would understand how it feels being a marginalized caste. Nevertheless, they do not transfer there own experience of racism with their own actions against homosexuals.

So my point is, being class conscious does not guarantee someone to become social conscious as well.