Asymptotic complexity of CDCL SAT solver that only selects negative literals
Not a direct answer to the question but, as DPLL can be seen as a special case of CDCL, hopefully of interest.

The problem of finding optimal branching literals for DPLL is (in a way) harder than SAT itself: the paper "On the complexity of choosing
the branching literal in DPLL" by Liberatore shows that 
choosing optimal branching literals in DPLL  is both NP-hard and coNP-hard.