Mark is right - I was using that combination, but usually on a 1D IV for an extra 1.3 crop factor. I also had a 70-200 f/2.8 and 24-70 f/2.8, 17-40 f/4 and 5D II.
I suggest you to take the longest lens you can, but I understand your concerns about weight and airline security. A 24-105 and 100-400 would be a good two-lens solution, with a 1.4 extender (you would lose auto focus capability with a 2x extender on the 100-400).
Some other points to bear in mind:
- Wildlife is most active at dusk and dawn, when the light is poorest. Be prepared to go high with the ISO.
- Dust can be a problem if you are changing lenses or inserting an extender. Two bodies helped me to overcome that issue, but a large zoom range is an alternative solution. Take a sensor cleaning kit.
- 24-105 will be fine for general purpose landscapes on a 5D III. You won't need anything wider. I only took a handful of shots with the 17-40, and most of those were at >24mm. Some of my landscapes (e.g. the herd of wildebeest on the plain) were shot at 420mm.
- Take some binoculars. You need to find the wildlife before you can take pictures of it (unless you are content with pictures of grazing ruminants or sleeping lions)
Have a great trip!
Edit - since you're going to Ngorongoro, you might be able to justify taking a 16-35mm to get a shot of the crater from the rim like this (except your crater will be bigger and have lots of wildlife in it)





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