Ethereum's current energy intensive Proof of Work is not used to run the smart contracts. It just secures the blockchain, same as Bitcoin. The smart contract execution power requirements are basically non-existant compared to that.
Not necessarily. The current verification algorithm doesn't have any useful side effects other than verifying that some amount of computing happened. That will even be true for whatever computation happens as part of proof of stake when it gets rolled out. In other words, and in either case, the only real effect of the computation that happens as part of the verification algorithm is the verification itself.
Edit: There's no reason to downvote OP's post, folks. It's a good question that some people may not know the answer to.