Conversational turn-taking is a complex communicative skill that requires both linguistic and executive functioning (EF) skills, including processing input while simultaneously forming and inhibiting responses until one's turn. Adult-child turn-taking predicts children's linguistic, cognitive, and socioemotional development. However, little is understood about how disruptions to temporal contingency in turn-taking, such as interruptions and overlapping speech, relate to cognitive outcomes, and how these relationships may vary across developmental contexts. In a longitudinal sample of 275 socioeconomically diverse mother-child dyads (children 50% male, 65% White), we conducted pre-registered examinations of whether the frequency of dyads' conversational disruption during free play when children were 3 years old related to children's executive functioning (EF; 9 months later), self-regulation skills (18 months later), and externalizing psychopathology in early adolescence (age 10-12 years). Contrary to hypotheses, more conversational disruptions significantly predicted "higher" inhibition skills, controlling for sex, age, income-to-needs (ITN), and language ability. Results were driven by maternal disruptions of the child's speech, and could not be explained by measures of overall talkativeness or interactiveness. Exploratory analyses revealed that ITN moderated these relationships, such that the positive effect of disruptions on inhibition was strongest for children from lower ITN backgrounds. We discuss how adult-driven "cooperative overlap" may serve as a form of engaged participation that supports cognition and behavior in certain cultural contexts.