It doesn't need anything in Web.config or user.config because it resolves the path to the db in the /App_Data folder .
public static string GetConnectionString()
if (ConfigurationManager.AppSettings["SqlCeApp_Data_FileName"] != null)
string path = System.Web.Hosting.HostingEnvironment.MapPath("~/App_Data/" + ConfigurationManager.AppSettings["SqlCeApp_Data_FileName"]);
string connectionString = "Data Source=" + path + ";Persist Security Info=False;";
The error is in initializing the type which seems more likely a problem with the hosting environment. SQL CE can work in Medium Trust hosting but your host may have a custom trust level that is more strict and that may prevent it from working.
I would check with your host about the trust level.