Webmethods Integration Server can integrate systems and orchestrate different web services from external systems on the network.
My question is: Is it possible to create Java code running in Webmethods Integration Server, and expose it as a web service? Therefore, having Webmethods host the web service.
yes that's possible. You can use a Java service inside IS to code your logic. You have to define an interface for this service (a doctype). After this is done, you create a webservice provider that calls your service. This applies to IS from version 7 upwards.