We theoretically explored the combined role of conformational fluctuations and quantum interference in determining the electrical conductance of single-molecule break junctions. In particular we computed the conductance of a family of methylsulfide-functionalized trans-alpha,omega-diphenyloligoene molecules, with terminal phenyl rings containing meta or para linkages, for which (at least in the absence of fluctuations) destructive interference in the former is expected to decrease their electrical conductance compared with the latter. We compared the predictions of density functional theory (DFT), in which fluctuational effects are absent, with results for the conformationally-averaged conductance obtained from an ensemble of conformations obtained from classical molecular dynamics. We found that junctions formed from these molecules exhibit distinct transport regimes during junction evolution and the signatures of quantum interference in these molecules survive the effect of conformational fluctuations. Furthermore, the agreement between theory and experiment is significantly improved by including conformational averaging.