I'm of the opinion that no, we will not. The computing power required to simulate a star (or a human brain, to go back down the analogy chain) is not there and will not be there, without some quantum computing magic. I doubt the sun provides enough energy for us to fully simulate the sun.

Simply running basic neural network is slow work, even with the best supercomputers we have today. Throw in the fact that a neural network is a super simplistic model of how we currently believe synapses work, and the scale of the simulation problem gets hard, fast.