I have written an application using the desktop sdk (12) accessing QB Pro. My customer is moving to QBES hosted on Linux. Will my app still work to their data? If so how is the connection done? RDS?
Yes, your app will still work.
With Enterprise hosted on Linux, just the QuickBooks company file/database/database manager components run on Linux. The actual QuickBooks application still runs on Windows.
QuickBooks SDK apps run alongside QuickBooks, and connect to QuickBooks directly, not to the database manager. So, your app will be installed on Windows, alongside QuickBooks, and connect to QuickBooks, which will in turn talk to the database/company file/database manager on Linux.