It would be remarkable if biological neural networks don't use gradient descent. They very likely do even if it is a highly approximate gradient. Neurons are optimizing for some objective, and the gradient is usually a very efficient way to do that optimization. It would be remarkable if evolution missed out on such a thing. Even simple Hebbian learning can be viewed as a gradient descent technique.

Gradients can be calculated in remarkably simple ways. Look at Hinton's recirculation networks for example.

I think you meant to say backprop.