IF we are talking about an ANN in a computer, then sure. It can be easily copied. But what about a grown network. For example, a network of resistors representing the weights, with a feed back loop that adjusts (continuously) the resistances during the learning process.

After the network has attained sufficient level of AI, we won't be able to read back the final value of resistances with the required precision. So the new network will still have to go thorough a learning process.