Does Enterprise Server and its associated adapters support double-byte. This is a requirement for our Japanese division?

I’m not sure if you refer to the Integration Server (IS) 4.6 or the Enterprise Server (ES) 5.0.1 since ES 4.6 doesn’t exist. In any case both Enterprise Server and Integration Server support double-byte.
Each component has a globalization statement in the readme that explicitely declares the current Internationalization level and any internationalization limitations. You can find each component readme in the Bookshelf section.
For your information, selected webMethods components are available in Japanese. You can find a list of the most recent Japanese releases in the product downloads section on Advantage.
Every recent adapter support the webMethods Internationalization Standard which includes support for double-byte. Sixteen of the 4.1.1 Enterprise Adapters are available in Japanese (user interface, help, documentation).