This article aims to contribute to the debate on the role of the Quota Law regarding the potential social mobility of students with high socioeconomic adversity, using administrative data from a federal university in Brazil. We used Confirmatory Factor Analysis technique to construct an adversity index, composed of variables that may negatively affect access to higher education, such as students' socioeconomic background, parental education, and ethnicity. We classified courses by expected earnings and assessed how background is associated with course choice. Then, we used regression models estimated by the Generalized Method of Moments (GMM) to identify the relative importance of the interaction between quota categories with the adversity index and the score on the admission exam (National High School Examination -- "Exame Nacional do Ensino Médio" -- ENEM) to predict course choice and consequent possibility of social mobility. The results showed that quotas can reduce the negative effects of socioeconomic adversity on social mobility. However, they are not completely sufficient to "break" the effects of the low quality of secondary education in relation to ENEM performance and, consequently, social mobility