This is possible due to the pluggable architecture of WSO2 API Manager, but this is not straight forward. The Gateway component of the API Manager handles Token Validation, Throttling, Caching and Mediation. Of these features Token Validation is configurable out of the box with any external Token Validating component since it uses Web service calls since it has a Web Service interface. The other 3 features will require customization at code level in order to function with Mule ESB. Therefore this is not the most recommended approach.
WSO2 API Manager can be used without an external ESB instance out of the box. So that would be the best way to use it.