Yes, it is possible to overwrite an existing output file in ArcMap ModelBuilder. Follow the steps below to enable overwriting the output file:
In some cases, when involving enterprise geodatabase or server connections, some tools fail to recognize the overwrite settings and return an error. This may be due to a known limitation of the software to overwrite outputs that reside in the in_memory workspace. As a workaround, save the output in a database connection instead of database server connection.