Numerous studies emphasize the potential indirect (genetic) benefits of polyandry in animals with resource-free mating systems. In this paper, we examine the potential for these benefits to fuel sexual selection and polyandry in the hermaphroditic ascidian Pyura stolonifera. Individuals were designated either sire (sperm producers) or dam (egg producers) at random and crossed in a North Carolina II breeding design to produce both paternal and maternal half siblings for our quantitative genetic analysis. We then partitioned the phenotypic variance in fertilization and hatching rates into additive and non-additive variance components. We found significant additive variance attributable to sire and dam effects at fertilization and hatching, suggesting the potential for selection to favour individuals carrying intrinsically 'good genes' for these traits. In separate analyses involving monandrous and polyandrous clutches, we found that both traits were elevated under polyandry, but the difference in hatching rates was due entirely to the difference in fertilization rates between treatments. When the hatching rates were standardized to account for variance at fertilization, there was no overall net benefit of polyandry for this trait. Despite this, we found that hatching success declined with increasing embryo densities, and that the slope of this decline was significantly greater in monandrous than polyandrous clutches. Hence, selection on embryo viability may still favour polyandry under restricted environmental conditions. Nevertheless, our results caution against interpreting elevated hatching success as an indirect genetic benefit of polyandry when variance in fertilization is not controlled.