Absolutely, dendritic trees are generally considered active and can elicit dendritic spikes. This 2-layer model is well studied in hippocampal CA1 neurons for example[1]. ANNs are far from reality but they do validate connectionism as probably the correct abstract model of learning. The thing that's harder to crack is plasticity i.e. the learning rules. Plasticity in real neurons is a very complex process and there is no indication that anything like backpropagation takes place.