Not if your system efficiency is limited by transmission and storage. Chemical energy (fuel) is more efficient and cheaper to store than electric energy, and will almost certainly continue to be an important medium in a post fossil fuel world.
Edit: I think I responded to the wrong post, but I guess I'll just leave this here as a general comment.
Really, when fossil fuels get more expensive you'd like a non fossil fuel based engine.
Efficient engines are incentivized by high fuel prices only as compared to less efficient fossil fuel engines.
Edit: I think I responded to the wrong post, but I guess I'll just leave this here as a general comment.