It may work but it is not the way to do it IMO. Transformers do weird things when they "talk" to each other like that. It could also burn up the t-stat. I do quite a bit of heating-cooling wiring and always keep a couple of "RIB"s (relay in a box) in the truck. Constantly getting me out of a jam (about $12 each).
http://www.functionaldevices.com/ChartPilot.html
