Neither the Elk M1G nor ISY works with a Nest, nor Ecobee (to my knowledge) directly. You need some other device in the middle such a Raspbery Pi or Homeseer. I use the latter.
My Nest for the main HVAC talks to Homeseer via a plugin for that software, but I basically never do anything with that connection as I just control the Nest with the iPhone / iPad app or via a browser if I wish to do so. The Elk is not involved at all, but I suppose it could, say, set back the heat when we arm the house away. We have an office at home for my wife and a heat pump, so that is almost never practical.
I do use another Nest to control a pellet insert, and have involved the Nest there in an interesting, Rube Goldberg way. I basically wanted to have automated and wireless control over starting that insert in the morning and setting it into one of three heating modes (Hi-Med-Lo) as it is used in my wife's office. I rewired the stove a bit to allow me to manually bypass the mode switch on the stove if I wished to do so, sending control to an Insteon four-relay device (cannot remember what they call it - EZ something). I then told the Nest it was controlling a gas furnace with 3-stage heat, and connected the output for each of those on the Nest to three relays (RIBs)' mounted in the Elk can and connected each of those to a separate zone on the Elk. So when the Nest calls for each of those three stages, it violates a zone in the Elk. I got this idea and basic wiring of relays (without involving an Elk) from a gentleman that goes by TwoBraids on one of the pellet stove forums (giving credit where due, as I would never have thought of it).
The Elk is connected to an ISY here, so when the Nest calls for any of the three stages and opens the related zone, the ISY can read that. I then use the ISY's programs to tell ISY to open the appropriate combination of relays on the EZ-whatever devices connected to the stove (including turning it on/off and setting the mode), and voila - automated pellet stove insert, with no ugly wires connecting it to the Nest, but with all onboard safety devices left intact (High temp limits, Proof of fire switches, etc.).
Now, all of that could be done without Homeseer, and frankly I had reached the point in my system where Homeseer was essentially unnecessary and used for nothing more than reading a few temp/humidity devices as a convenience. But the one problem with the setup described above was that once the pellet stove reached target temp on the Nest, it would just turn off, as that was what it was designed to do even with its regular, hard wired thermostat. What I really wanted it to do was to go into the Lo mode and just "idle", keeping the office within a degree or two of the target temp, avoiding a drop below the target temp in most cases, and also saving the stove from cycling on and off, which chews through ignitors. So, I set up an output in the Elk that could be turned on by Homeseer when the stove was at or near target temp (70 - 72). I then updated my program in the ISY to enter Lo mode on the stove when that output was turned on, but to allow it to go to a higher mode if the Nest called for stage 2 or 3 heat, or to turn off the stove if the room temp exceeded 72.
The result is complete control of the pellet stove through the Nest (which my non-techie) wife can easily control, and a more even temperature in that office area, with less cycling of the stove on and off. It is working perfectly, and if I want to revert back to manual control of the stove, I just flick a toggle switch I installed that returns mode control to the manual switch on the stove.
Sorry for the long write-up. I may post that somewhere else on the forum in case anyone else wants to hack their pellet stove to use a Nest, etc.