Using WSDL, can we generate other public methods inside a class that is a parameter of a Web Service Method?

No - not with web services. The system metaphor with web services is message passing. There is a client and a server and they exchange messages via a pre-arranged communication protocol or contract.

The messages and the exchanges are described in WSDL. What you are imagining is a distributed object system, where you transmit objects and not messages. This is generally not the model that web services tools (for any platform) support.

Consider changing your architecture to use DTOs - Data Transfer Objects - for the things that get exchanged. Then implement logic in different business-level objects that maybe use the Adapter pattern to slurp their state from the DTO. The business objects could be shared data types, if you like; in other words a single JAR that defines the type and gets referenced from within client and from within server.

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