Answer
José María Giménez has not won the Copa América with Uruguay. He has been a member of the Uruguay national team since 2012, and has represented them at the 2014 and 2018 FIFA World Cups, as well as the 2015 and 2019 Copa América tournaments. However, Uruguay has not won the Copa América since 2011, and Giménez has not been on the team that has won the tournament.