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I did exactly what you described. I spent 30 days doing volunteer conservation work, mostly in Botswana, but also spent a decent amount of time in South Africa. I added on an additional few days in-country to do some more personal stuff (a safari).
Calling it volunteer work is a bit of an oxymoron. More like pay-to-volunteer work. There are no "free" programs, especially for primates or the big cats. You have to pay, a considerable amount, for the privilege of "volunteering." In fact, it was by far the most expensive month of my life, and I could have bought a car for what I paid, although the safari cost a considerable amount (absolutely worth it).
It is essentially a great way to see "wild" Africa, not entirely as a tourist. I would recommend it, but make sure you understand what you are getting into. These programs do not need volunteers to help with serious scientific work. They need rich Americans to pay them what is a small (maybe large) fortune in Africa, for the experience of being in Africa and perhaps aiding a bit with some research. There are several outfits that rely entirely upon "busy work," work that does not need to be done and that serves no purpose to anyone, to keep their paying "volunteers" busy. I know of one outfit in general that does daily game counts in a fairly small area, and while this is interesting to go along on, the data gathered is of use to no one, and most likely is not even reported.
Overall it was a positive experience, but I have always been fascinated with Africa. I intend to return many times, although not for conservation work. Feel free to PM me for additional details, such as the operation I went with.
Then absolutely go for it! My one recommendation would be to absolutely steer clear of anything in South Africa. SA is the "tame" version of Africa. Everything, and I do mean everything, is behind a fence. Yes, these fences are big....but the environment is controlled. If you have driven through Texas, or are familiar with deer hunting, SA is the Texas of Africa. Botswana is a solid choice, as is Tanzania. A more jungle type experience would be interesting as well, such as Cameroon. Zimbabwe is of course not an option, due to Mugabe. Kenya is another good choice, and for one reason or another Kenyans particularly love Americans.
Don't be afraid to look into other options while you are there. The airfare is so costly, you might as well kill two birds with one stone. If there is something you have always wanted to do or see (such as Victoria Falls), add it on. This can take a lot of research, but it was absolutely worth it for me. There was no way I could see going all the way to Africa without living my dream of a safari.
Like others have said, Africa is a whole other world. I adapted as much as I could while I was there, going barefoot almost everywhere and venturing out into the bush on my own repeatedly (very much against the wishes of the person in charge). I did have one sketchy experience getting mauled by a poisonous fish....long story. It is an interesting experience to go to town and walk around the mall in bare feet with a knife on your side. I picked up just enough of the local language that I could almost pass as a local, if I didn't speak much. I didn't go in "green," as I have studied Africa and Africana extensively. You will have a great time, and it will not be anything like what you expect - those two things are for sure!