Even the popular Nest thermostat claims to work without a C-wire, there are some issues. Without a C-wire, the Nest gets its power from your heating or cooling system when it’s running. When it’s not running, the Nest still needs to get juice. It will “pulse” the heat wire, turning on the furnace for a moment to pull a bit of power to keep itself going.
In some systems, this is unnoticeable, but in others, the furnace responds as if being told to turn on and then immediately off. Not to mention this will drastically reduce your furnace PCB life expectancy (and it is very expensive to replace).