Yes we do, however we do not support Create/Delete database permission. So in order to use Code First, you'll also have to use EF Migration. For more information about EF Migration, please visit http://blogs.msdn.com/b/adonet/archive/2012/02/09/ef-4-3-code-based-migrations-walkthrough.aspx
You can compile your application locally and then restore your database onto our server when you move your application to our hosting service. You can restore your database via our control panel.