Please refer to the attached screenshot and sample video.

Workaround:
public class CustomGrid : RadGridView
{
    public override string ThemeClassName  
    { 
        get 
        { 
            return typeof(RadGridView).FullName;  
        }
    }

    protected override void OnKeyPress(KeyPressEventArgs e)
    {
        this.BeginEdit();
        if (this.GridViewElement.ActiveEditor is RadDropDownListEditor)
        {
            string symbol = e.KeyChar.ToString();
            RadDropDownListEditor editor = this.GridViewElement.ActiveEditor as RadDropDownListEditor;
            RadDropDownListEditorElement element = editor.EditorElement as RadDropDownListEditorElement;

            if ((element.AutoCompleteMode & AutoCompleteMode.Suggest) == AutoCompleteMode.Suggest)
            {
                element.EditableElementText += symbol;
                element.EditableElement.SelectionStart = 1;
                element.EditableElement.SelectionLength = 0;
            }
        }
        base.OnKeyPress(e);
    }
}