It is obviously true that the worst-case runtime of a problem on n variables and m clauses is O(m2^n), and that the brute-force algorithm can be sharded out to 2k cores and run in time O(m2^(n-k)). If your approach is brute-force, yes, you might as well use this technique.

But, notice that a shard whose k preset bits are in direct conflict should take zero time -- it's smarter to detect a conflict and terminate than carry on computing all 2^(n-k) invalid assignments. Each such conflicting shard decreases the benefit of your parallelization -- a depth-first solver wouldn't spend almost any time on that particular branch, but you've wasted a whole core on it.

The real question is, what if your algorithm is smarter than brute force? Such algorithms may spend considerable time preprocessing, which is not trivially parallelized, resulting in many cores duplicating tons of work with very little effective speedup.