The RadAutoCompleteBox control is populated with data, base on the entered in the input text. Therefor, opening the DropDown, when the control is focused would display an empty DropDown, which I believe is not the intended scenario. I can suggest you to use the RadComboBox
control, which would fit the requirements of your scenario.
the Telerik team
If you want to get updates on new releases, tips and tricks and sneak peeks at our product labs directly from the developers working on the RadControls for ASP.NET AJAX, subscribe to their blog feed