The extenders, aka teleconverters are lens attachments that fit between the lens and the camera body and multiply the focal length by 1.4 or 2. Better suited for fast primes with good IQ. An extender, attached on a poor IQ zoom will produce even poorer results. Many people put low quality TCs on poor quality zooms and this has generated a very bad reputation for TCs.
You should not consider taking a 200 lens and doubling it's focal length with an extender as a means to reach 400mm when you really might need 500mm. The correct approach is to select a lens that covers 80% of your reach needs and then use a 1.4xTC to get that little bit more when it is needed.
If you find you need a 2xTC too much, then it means you really need a longer lens. Of course, this might not be easy with bird photographers using their 600mm lenses with the 2xTC attached all the time. Well, they really need a longer lens, but $80,000 for a 1000/5.6L (without IS I think) is not really appealing.
Trust me, you will get much better results with a Tamron 200-500 than with a 70-300 + 2xTC.