Yes, I did exactly what you described (pic below).
I ended up building a TSS2 unit to simplify needing to consider my basement's ambient temperature and fermentation heat to decide in using cooling vs heating mode. A dual stage controller is GREAT. I still put switches to disconnect power from the relay outlets to deal with cold pitching and lagering and not need to go into the device to change parameters. It will keep very tight temperature to the setpoint control with both relays on.
The A419 is now on heating mode to create a conditioning zone in my cold MN basement. It's primary use is bottle conditioning, but is also useful for storing an ale at a stable temperature and get it out of my fermentation chamber. I recently used it to do a yeast starter on a stirplate in the heated box at 68F instead of in the kitchen.
See Posts #80, #83 & #84 of this thread for some data-logging experience with the A419 & TSS2 for applications where the probe is on the side of a carboy/bucket and insulated over.