SQL Server Management Studio Express and MySQL?

It will not works with MySQL.The name of product is "SQL Server Management Studio", so it manages SQL Server instances.

If you need tool with similar functionality, try Toad for MySQL, it's freeware or Oracle SQLDeveloper.

I don't know if you found the answer yet, but the following links can help:

1- HOWTO: Setup SQL Server Linked Server to MySQL
2- Creating Linked server to MYSQL from SQL Server

I can't see how this will ever work, SSMS is written only for MSSQL.

You can however create a link server to the mysql database and use it that way, I doubt intellisense will work though. see here for more info.