Hi Leon,
I am not sure I got what you'd like to achieve, but maybe the following will help:
-- TestComplete can operate only on the machine where it is installed;
-- TestComplete can operate unattended if it does not need to interact with the UI. Otherwise, see the
http://support.smartbear.com/viewarticle/56550/ help topic;
-- You can use TestComplete installed on the remote box via Remote Desktop. See
http://support.smartbear.com/viewarticle/55606/ for more details;
-- While TestComplete can perform coordinate-based clicks over the Remote Desktop window, the window itself is just an image. Thus, it does not provide any info about applications running on the remote computer and thus only image-based search is possible within this window.