A:Answer Technically yes, but personally I wouldn't want to do that, as you'd be putting stress on the hard drive and whatnot, powering them up and down. Plus of course it would then be unavailable to record new shows if anything's scheduled (unless you plug in an antenna at the new location each time).
IMO a better way to do it would be to also buy a Tivo Mini, which lets you stream shows from your Tivo to another TV in your home using your network. A lot more convenient, and then you wouldn't be powering it down all the time.
As far as the Internet part of that goes, Tivos need an Internet connection in order to update their program guides (older ones also worked with phone lines, but the newer ones don't). BUT the shows already on there continue to work just fine regardless of whether they have an Internet connection or not. Normally the Tivo will automatically check for updates about once every 26 hours, and has about 2 weeks of guide data, so can technically be disconnected from the Internet for close to 2 weeks and still have guide data for recording. Of course networks often make weird last minute changes to their schedules (which seems to be happening a lot lately) and the Tivo wouldn't get those if it's disconnected from the Internet.
