If its about bag space and weight just get a teleconverter for the 70-200. Honestly for wildlife I would rather just use the 70-200 and crop than use the 100-400. The Tammy does well focusing in my experience.
I tried the 7D / 70-200 f2.8 IS II / 2X III combination. Intitial shots showed severe Front Focus Issues, so I exchanged that extender for another. I really wanted this combination to work for me, so I tackled lens Microadjustment. What I discovered was that at 400mm, the setup was fairly accurate, (although also somewhat inconsistant) with little or no adjustment needed, but at 200mm I needed to adjust focusing to +12 on the -20 to +20 scale. I decided this was not going to work for me, so I returned the second extender.
The reason I purchased the 70-200 in the first place over the 100-400, was I felt I could use the 2X extender to get to 400mm. Eventually I will probably end up getting a 100-400.