Animal Kingdom is my home resort with DVC, and I've stayed there more than any other Disney resort. The animals are always very active on the savannah, but they go where they want to go. They might be hanging out near your room, or another room. But they do actually live on the savannah. They have the option to go in for checks every morning, but it's up to the animals themselves. (I did the on-site safari years ago, and learned that the animals are trained to react to woodblocks being banged together as a call to come in to the stables for check-ups. But it's voluntary on the animals' parts.)
Savannah view is worth it, if you want to see animals from your room. But also keep in mind that there are viewing areas ALL over the resort, so you can still watch the animals, even if not from your balcony.