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It's worth it. It also works excellently on the 100-400 L, which I have, though because that is nominally f/5.6 as far as the electronics are concerned for AF, I have to manually focus it.
Personally, I'd use the 70-200 L at 200 without the tele-extender than the 135 with the tele-extender. Get the 1.4x II for the long end of the 70-200 so you'll have a very good 280 mm lens.