Workaround: create a custom RadMultiColumnComboBox control with a custom element. You can also check the attached project.

public class MyRadMultiColumnComboBox : RadMultiColumnComboBox
{
    public override string ThemeClassName
    {
        get
        {
            return typeof(RadMultiColumnComboBox).FullName;
        }
    }

    protected override RadMultiColumnComboBoxElement CreateMultiColumnComboBoxElement()
    {
        return new MyRadMultiColumnComboBoxElement();
    }
}

public class MyRadMultiColumnComboBoxElement : RadMultiColumnComboBoxElement
{
    protected override Type ThemeEffectiveType
    {
        get
        {
            return typeof(RadMultiColumnComboBoxElement);
        }
    }

    protected override void ProcessKeyDown(object sender, KeyEventArgs e)
    {
        base.ProcessKeyDown(sender, e);

        if (this.IsPopupOpen && (e.KeyCode == Keys.PageDown || e.KeyCode == Keys.PageUp))
        {
            this.EditorControl.GridBehavior.ProcessKey(e);
        }
    }
}