So, normally in order to do this, you need a device on either end: one to inject the DC current, and then one on the other end to pull the DC current off and clean the AC back to normal (non-biased).
In the case of the Nest couple with the Google Power Connector, these two devices would be working together to accomplish that.
Also, whether or not that is what is happening is purely a guess (I do not have a Power Connector and have not tested what it is doing myself). It would be a reasonable engineering solution. However, there are also other engineering solutions like switching to a pure DC solution with low-level signaling between the Nest and the Power Connector whereby the Nest gets power and then signals to the Power Connector to operate the 24VAC relay connected to the furnace. The Nest would then look at the R/W pair and see what kind of voltage/signal is present and then operate in the appropriate mode. If it senses there is 24VAC present, then it operates in regular thermostat mode, if instead is senses something like 3VDC, then it might send a low-level coded signal to the other end to check if it's connected to a Power Connector.
If you are up to experimenting, what you could do is with a basic voltmeter and the Power Connector wired in, check the AC voltage between Power Connector's R wire going to the Nest and the transformer (C)ommon. If it does read 24VAC, then it's likely there is a DC bias... You can then switch the voltmeter into DC mode and see if it shows a DC voltage between the R and W wires from the Power Connector to the Nest (and depending on which wires you randomly tested +/- with the voltmeter, it may read a + or - voltage).
If instead, you read no AC voltage (or very minimal < 1V), but you do read a DC voltage, then it's more likely the Power Connector is sending DC power and communicating with a low-level signaling protocol.
I would be very curious to know what you find on this.
