Philipych, like you I also assume that TA-10/TA-20 "are not simply battery charger, and at the same time serves as an antenna-feeder path", ie, assume that it serves as an antenna probably, but it has an extra function besides feeding the battery: energizing the traffic receiver, this is the hypothesis.
In short, what I meant was that the receiver built into some models of garmin PERHAPS work with other vehicular GARMIN CABLES (or other duly modified) have they or not antenna. An example of cable "alternative" was the cable that I mentioned and was indicated as a substitute to TA-20 by Garmin and which, it appears, has no antenna. All this because the receiver only works with a power cord connected, strong principle it depends on external power line from a cable. With other Garmin original cables if it works, will certainly be in a limited way, as backup for emergencies or for testing. Of course just only testing with any other vehicular cable from Garmin to check this hypothesis. Also in the Traffic Receiver Status screen you can check if the receiver is initialized and the intensity of the tune.