I would not advise it.. Yes, the situation you're in sucks and is probably illegal. But if you manually turn on the heat by connecting Red and White, it will heat the upstairs, which could bring on the a/c, and putting the heat from gas furnace through a running a/c evap coil could cause a compressor failure, which you would be accountable for if you get caught. That said.. If you disconnect the Red wire from the circuit board so no power gets sent to the thermostat upstairs, that would solve that issue. You could even run a new Red to your own thermostat if you wanted. But it's probably only a matter of time before they realize their stat isn't working and call maintenance.