Powering Arduino from 12v 1A linear regulator?

Tobster86:
Yeah the RS ones require an inductor, a capacitor and a diode, although I can design these into the circuit without too much bother.

Just to be 100% clear; will the Arduino function as normal from 5V by simply supplying 5V to it's 5V pin and leaving the Vin pin disconnected?

Not so simple to give a definitive answer.
Many do just that with no problems reported. However be aware that the official Arduino recommendation is to not do that. From the product page description:

5V. This pin outputs a regulated 5V from the regulator on the board. The board can be supplied with power either from the DC power jack (7 - 12V), the USB connector (5V), or the VIN pin of the board (7-12V). Supplying voltage via the 5V or 3.3V pins bypasses the regulator, and can damage your board. We don't advise it.