Another workaround is to called the Populate method from within a Dispather:
private void RadAutoCompleteBox_GotFocus(object sender, RoutedEventArgs e)
{
    var auto = sender as RadAutoCompleteBox;
    Dispatcher.BeginInvoke(new Action(() => { auto.Populate("searchText"); }));
}

Workaround:
Use the LocationChanged event of the parent Window instance and set the IsOpen property of any Popup instance related to the RadAutoCompleteBox to False. The next code snippet shows the described workaround:

In the XAML code:
<Window LocationChanged="OnWindowLocationChanged" ...>
      <telerik:RadAutoCompleteBox x:Name="AutoCompleteBox" .../>
</Window>
In the event handler:
private void OnWindowLocationChanged(object sender, EventArgs e)
{
    var popups = this.AutoCompleteBox.ChildrenOfType<Popup>();
    foreach (var popup in popups)
    {
        if (popup.IsOpen)
        {
            popup.IsOpen = false;
        }
    }
}