I have tested joining table data within the default ArcGIS Server Manager web application builder, and it appears that the linked table data carries over in the web application as long as the table is in the same database as ArcSDE connection (or may possibly even work linking to a table within another database through an OLE DB connection in the map document, but am unsure).
Does anyone have an idea how to recreate the "Joined table" link in the Javascript API?