Hi John,
For travelling 3rd World Countries especially when hauling heavy loads at the same time, I would always go for a 26" bike with a steelframe and no suspension. Your question if it is generally possible to do it on a 27" touring bike: yes it is. It just depends on your travelling (and maintenance-) preferences. Without having been there myself, I believe you need to be prepared for bad road conditions - especially the poorer the countries, the worse the road conditions. In Sudan, for example, there are streches where there are no roads at all, so you need to follow the railway or take a truckride. Also, when the rainseason starts you will get problems with mud due to unsealed roads.
In general, there is no perfect bike to a trip like this: in some areas you're better off with a light and fast touring bike, and then there are areas where you would need an MTB for heavy duty purposes. Also, it's pretty much up to one's personal taste what to ride or which equipment is seen to be needed.
Greetings,
Andreas