No, you can't extend the list of properties, and this is complicated by the fact you use Winforms that has a poor UI Automation support (it uses IAccessible with bridges etc.).

What you can do though is add some fake objects to the automation tree, for example, here is a sample Winforms UserControl that does it:

public partial class UserControl1 : UserControl
{
    public UserControl1()
    {
        InitializeComponent();

        Button button = new Button();
        button.Location = new Point(32, 28);
        button.Size = new Size(75, 23);
        button.Text = "MyButton";
        Controls.Add(button);

        Label label = new Label();
        label.Location = new Point(49, 80);
        label.Size = new Size(35, 13);
        label.Text = "MyLabel";
        Controls.Add(label);

        MyCustomProp = "MyCustomValue";
    }

    public string MyCustomProp { get; set; }

    protected override AccessibleObject CreateAccessibilityInstance()
    {
        return new UserControl1AccessibleObject(this);
    }

    protected class UserControl1AccessibleObject : ControlAccessibleObject
    {
        public UserControl1AccessibleObject(UserControl1 ownerControl)
            : base(ownerControl)
        {
        }

        public new UserControl1 Owner
        {
            get
            {
                return (UserControl1)base.Owner;
            }
        }

        public override int GetChildCount()
        {
            return 1;
        }

        public override AccessibleObject GetChild(int index)
        {
            if (index == 0)
                return new ValueAccessibleObject("MyCustomProp", Owner.MyCustomProp);

            return base.GetChild(index);
        }
    }
}

public class ValueAccessibleObject : AccessibleObject
{
    private string _name;
    private string _value;

    public ValueAccessibleObject(string name, string value)
    {
        _name = name;
        _value = value;
    }

    public override AccessibleRole Role
    {
        get
        {
            return AccessibleRole.Text; // activate Value pattern
        }
    }

    // note you need to override with member values, base value cannot always store something
    public override string Value { get { return _value; } set { _value = value; } }
    public override string Name { get { return _name; } }
}

And this is how it appears in the automation tree (using the inspect.exe tool):

Note this technique also supports writing back to the property because it's based on the ValuePattern.