Override .NET's source for AppSettings (hacky, don't use this at home)

KeyVaultConfigSystem.cs

public sealed class KeyVaultConfigSystem
    : IInternalConfigSystem
{
    private const string AppSettingsKey = "appSettings";

    private readonly IInternalConfigSystem _internalConfigSystem;
    private object _appSettings;

    private KeyVaultConfigSystem(IInternalConfigSystem internalConfigSystem)
    {
        _internalConfigSystem = internalConfigSystem;
    }

    public static void Install()
    {
        // Make sure ConfigurationManager is initialized
        // ReSharper disable once UnusedVariable
        var temp = ConfigurationManager.AppSettings;

        // Set KeyVaultConfigSystem as ConfigurationManager's IInternalConfigSystem
        // https://github.com/Microsoft/referencesource/blob/master/System.Configuration/System/Configuration/ConfigurationManager.cs#L19
        var configSystemField = typeof(ConfigurationManager)
            .GetField("s_configSystem", BindingFlags.Static | BindingFlags.NonPublic);

        if (configSystemField != null)
        {
            configSystemField.SetValue(null, 
                new KeyVaultConfigSystem((IInternalConfigSystem)configSystemField.GetValue(null)));

            return;
        }

        throw new NotSupportedException("Can not set ConfigurationManager's internal configuration system.");
    }

    public object GetSection(string configKey)
    {
        if (configKey == AppSettingsKey && _appSettings != null)
        {
            return _appSettings;
        }

        object internalSection = _internalConfigSystem.GetSection(configKey);
        if (configKey == AppSettingsKey && internalSection is NameValueCollection)
        {
            // Create a new NameValueCollection
            var mergedConfiguration = new NameValueCollection((NameValueCollection)internalSection);

            // Inject our own settings
            mergedConfiguration["MySampleSecret"] = "Hello from custom config system";

            // Store for future use
            _appSettings = mergedConfiguration;
            return _appSettings;
        }

        return internalSection;
    }

    public void RefreshConfig(string sectionName)
    {
        if (sectionName == AppSettingsKey)
        {
            _appSettings = null;
        }

        _internalConfigSystem.RefreshConfig(sectionName);
    }

    public bool SupportsUserConfig
    {
        get { return _internalConfigSystem.SupportsUserConfig; }
    }
}

Program.cs

class Program
{
    static void Main(string[] args)
    {
        KeyVaultConfigSystem.Install();

        Console.WriteLine(ConfigurationManager.AppSettings["MySampleSecret"]);
        Console.ReadLine();
    }
}