I have a feature that is boolean and I would like to feed it to a neural net as one of the inputs. I think in theory the best is to encode as false->0 and true->1 because 0 as an input will deactivate weights of a neuron. Is this correct?
Actually, it is not clear what you mean by deactivating but if it means the output of neuron would be zero, it is not correct due to having bias term, also known as intercept. Furthermore, we usually use normalisation for features which are of different scales. Your boolean values do not have a large range. You don't need to scale them. If I want to be more precise, you may need depending on the other features' range, because they may change slightly among different input patterns and vary less than let say 1e-5 for different samples, but most of the time, booleans are not needed to be scaled.