Please refer to the attached gif file.

Workaround: close manually the drop down list when the auto-complete popup is shown:

    this.radDropDownList1.AutoCompleteMode = AutoCompleteMode.SuggestAppend;
    this.radDropDownList1.DropDownListElement.AutoCompleteSuggest.DropDownList.PopupOpened+=DropDownList_PopupOpened;

private void DropDownList_PopupOpened(object sender, EventArgs e)
{
    this.radDropDownList1.CloseDropDown();
}