well a thermostat is actually a really simple device, so it's pretty easy to test on a workbench without needing to connect to your HVAC. Either simulate temp changes with a pot or use a heat lamp and fan, and you're off and running. For mine I have a 24VAC power supply (which is what the HVAC supplies) on my workbench and some lights connected to the relays. In theory it should translate pretty well to actual installation on the wall, when the time comes. To more directly answer your question, I have not tried to run it in tandem with the existing thermostat. In practice it might be feasible but in my mind it seems like unnecessary complication 
I like the IOIO too, but the issue I have with just implementing the androidthermostat.com project as it stands is the android device itself. I don't want to rely on the android to keep my HVAC running, especially since the phones are aging and could potentially fail at any time. The IOIO doesn't work without an android device, so I want to use an arduino. The code he wrote is pretty good, especially the API. I just need to port it such that instead of handling all of the scheduling and decision making itself, it sends an updated schedule to the arduino when changes are made. Rather than directly turning things off or on, it tells the arduino that the action has been requested. That sort of thing. If I'm successful with that, the android device can fail without the HVAC control being completely lost or worse, leaving the heater or AC on well past it's defined shutoff point.
One perceived advantage of using the android device to control the arduino thermostat was the built-in wifi radio. That should alleviate the need to connect the arduino directly to my network... but the more I think about it I may end up doing that anyway. I'm using Due boards, so I don't have to worry about stacking a host shield and an ethernet shield - the host capability is built on to the Due mainboard.
So many projects, so little free time