TabHost seems to be supported, while I am not sure about Activity Group. I would recommend to read the http://support.smartbear.com/viewarticle/62608/ help topic for more details.
When I try to automate our app I noticed that TestComplete can detect only the controls in the first screen (Login) and second screen (Main). All other screens TestComplete cannot detect the controls anymore even the common ones such as textboxes and buttons.