Would this fry my Arduinos?

jeffd:
Ok, but the mA of the combined batteries wont be too much? Its my understanding that voltage will stay at 9V because they are in parallel?

No they are not operating in parallel mode, because each board has a seperate wire going to just one positive terminal of one battery. Your arrangement is just allowing one switch contact to turn on or off all three boards at the same time. If you want the batteries to operate in true parallel then all positive terminals should wired together and all negative terminals should be wired together. Then have one wire from these positive terminals to one side of the switch, and then have three wires from the other side of the switch to each of the individual arduino Vin pins. That way the batteries will discharge as one larger battery rather then each discharging at a different rate depending on each specific board and it's shields and external circuitry.

Just for educational purposes (im still learning), whats the advantage of having the switch on the common ground rather than a common + ?

No advantage, but same effect of single switch turns all on and off, also not true parallel operation, do as above instead.