Adding FAN feature to oil furnace from thermostat
To answer the first question, YES. I have lived in my house for 18 years and the furnace fan has run for 18 years continuously. For the 2nd question, yes: attach the green wire to the thermostats G terminal, use it to power a relay coil (24 volts), and wire the contacts of the relay as you stated. Check all wiring before turning the power back on.