(Rewritten to make clearer.)
Once you have the program installer in hand, the installer and program have no need to connect to the Internet for installing and running the program. A registration check is done each time that the program is run and is done using code that is internal to the program. A machine with a TMG installation never needs to be connected to the Internet.
Related to this, does the TMG installer have any inbuilt count of how many installs I have done in order to ensure that the number of installs does not exceed a licensed maximum? If it does, then eventually as I continue to replace my hardware over the coming years and reinstall TMG on the new hardware each time, am I eventually going to be stopped from doing that by the installer? I wouldn't want that scenario to eventuate years after TMG support has long gone.