You would need to create a plugin. You could create a plugin using hook location newpost_process and do something like:
Code:
if ($foruminfo['forumid'] == ID)
$dataman->set('visible', 1);
(changing ID to your tech support forumid), but I think that logic is a little too simple and doesn't handle every case (like if the thread is hidden and a moderator is replying, then you'd want it to stay hidden). It would take some time to work out all the logic and I don't have time right now, but maybe someone else can, or maybe you can try it with the above code and see if it works out for you (maybe the special cases don't happen often enough to cause trouble).