Yes, easily done with a RELAY board, but not with the one you linked to, that uses MOSFETS. Open the remote and connect the dry contacts of the relay to the wires going to the push button of the remote. The relay will function as the push button. One thing to keep in mind though, it's not 100% reliable because it depends on the heating cycles of the fog machine. If it's in a re-heat cycle when the controller closes the relay, you won't get any fog. For the most part, it works pretty well. Also, be sure to isolate the relay board and connections.