last week a friend and I put my 1.4x II
extender and his 100-400L together and used it on a tripod, taking photos mainly of light aircraft.
With an aperture of 5.6 at the top end (above 250mm), the 1.4x will set you back to F8, the 2x even to 9.5. In both cases you loose autofocus, which made handling quite difficult, given the fast movements of the aircraft.
I personally don't think that you will have much fun with the 100-400 with 2x extender,
1) because it becomes a very slow lens with F9
2) it will be quite difficult to handle with such a long effective focal length and manual focus.