The main liability with the whole Wizard+Computer equation (aside from it being non-canonical, but that is waived for the purposes of discussion) is something physical crossing whichever Circle happens to be extant.
With a wireless keyboard/mouse and a rechargeable laptop computer (unplugged, in a Circle) accessing the Internet wirelessly, with the wireless transmitter some distance from the Wizard, this is theoretically plausible, though has ergonomic/vision challenges for the user - also, keyboards and wireless routers will need replacing regularly. Integrating a USB-powered projector would allow the laptop to project to a screen large enough for the Wizard to see more effectively, but would run down the battery more quickly.
The Butters-GPS example is a common component of these discussions, so it should be taken as understood that wireless signals aren't Circle-breaking. Nor should light be - electronic or otherwise. Power cables, however, are, and that's the most obvious barrier. Without reliable access to power, peripherals are limited: you can't really hook up a large-screen monitor or a printer.