I just did this tour last week. As others have said, as long as the phone can be tied to you with whatever they give you, you can take it. We opted to leave our phones in the lockers. They do take a lot of pictures. However, at one point, dh and I both wish one of us would have had a phone. I would have liked to have gotten a few more candid shots of my kids. The pics they took on the tour were awesome though--better than anything I have ever gotten from a Photopass photographer. They will take a shot of anything you ask and got lots of my family. A couple people on the tour took nice DSLR cameras. I own several DSLR cameras, and don't think I would have wanted to lug that along.
Side note--the Wild Africa Trek was the coolest thing we have ever done at Disney!