No, the sinking of mid-ocean ridges into ocean trenches does not prove Continental Drift theory. Continental drift theory states that the continents have moved relative to each other over time. The sinking of mid-ocean ridges into ocean trenches is a process called subduction, which is part of the process of seafloor spreading and the formation of new ocean crust. While the processes of subduction and seafloor spreading are related to continental drift, the sinking of mid-ocean ridges into ocean trenches does not directly prove Continental Drift theory.