||Joins that use ODBC/OLE DB connections on Windows are not supported by the ArcMap server on Unix (ArcIMS and ArcGIS Server). ArcObjects rely on OLE DB libraries to access data when connecting to databases directly. However, OLE DB libraries are currently not implemented on Linux or Solaris.
Here are some alternative suggestions:
1. If size of the data permits, the table could be referenced as a DBF file, which is periodically updated (by an operating system scheduled task, for example) from the MySQL table. In such case, a non-pooled service should be used to get the map data updated upon each session.
2. Your table data could be managed by a database system which is supported by SDE. If you require an open-source database system, PostgreSQL could serve such task.