They ask that you not take flash pictures, for the safety of the performers, but just like every other attraction that advises that, idiots take flash photos anyway. It always cracks me up, because you know they all get home and have a perfectly illuminated photo of the back of the heads of the people in front of them, with a blurry dark image of the show behind. LOL!
So yes, you can take photos. You can even video tape it if you want, although I've tried and it's very difficult to get nice shots from a night show. You really do need a tripod and to set the shutter speed very slow or light setting to low light. The video is especially tough since the stage is so large -- I hate to move the camera around too much and it's almost impossible to catch the whole show without doing that.