I don't think a 70-200mm + 1.4x TC is the way to get to 280mm, and a 70-200mm + 2x TC is definitely not the way to get to 400mm. Compare the 70-200mm f/2.8 non-IS with the 100-400mm at 400mm f/5.6 (
ISO 12233 crop link). The 70-200 f/2.8 non-IS plus 2x TC costs the same as the 100-400mm, lacks IS, and is quite optically inferior. The f/2.8 IS version + TC costs significantly more than 100-400mm, and still optically worse. The 70-200mm f/2.8 IS MkII + TC is even more expensive (pushing $1K more than the 100-400mm), and while the 70-200 II holds up better to a TC than any other 70-200 zoom, it's still not as good as the 100-400mm @ 400mm (although the MkII + 1.4x @ 280mm is as good as the 100-400mm @ 300mm - which is why I use the 70-200 II + 1.4x as a bird/wildlife lens
when it's raining (but when it's dry, I use the 100-400mm).
An extender is useful if you only rarely need that focal length. If you regularly use a particular focal length (and for birds/wildlife, you will regularly use 400mm), then get a lens that natively covers that focal length (the few possible exceptions being the fast supertele primes, e.g. 300mm f/2.8L, 400mm f/2.8L, etc., which lose very little optical quality by adding a TC).