I doubt an i7 will make much difference, a decent i5 will be more than fast enough. In fact, I found the higher clock speed of my i3 more beneficial than the slower clocks of the Xeon E3 I had - dual core 3.6GHz with HT was better for running Plex than quad core 3.2GHz.
Once the drives are spun down, I'd fully expect a modern Haswell build to idle around 25W. Certainly my i3 on the B85 board idles at 22W, though it only has a single i218 NIC and two fans and a 300W PSU. Even when I was running the Xeon E3-1225v3 on the Asus P9D board which had IPMI, dual NICs, etc, idle power consumption was still only 30-32W.
With idle power consumption that low, you'd need to be very penny pinching to go to the effort of shutting it down.