I don't think that Boob Tube does mean watching TV. TVs have slang names like telly, the box, the idiot box, and the tube. The tube because behind the screen is a cathode ray tube that opens up to make the glass screen. (Correct me scientists, if I am wrong). A Boob Tube is a tight fitting sleeveless top for ladies.
In 1969, the 'Daily Telegraph' published an article in which the TV was referred to - in a sort of fake Americanism - as "the boob-toob". That was the earliest recorded use of 'boob tube' (properly) in the way you suggest, JP. The idea behind it is that television is entertainment for idiots, with one of the meanings of 'boob' actually being 'idiot'.
Common usage here in the US would equate the television set to the boob tube. The boob would refer to the viewer; the tube would refer to the television screen. A boob is a stupid person, although the term is not very current. You have to love the rhyme of these derogatory names.