you can usually just change the top of the valve without any draining its usually just the motor that goes not the mechanical part of the valve
In this case there is roughness in the valve, so it might get him through winter but it’s possible it will fail quickly.
Having said that, I’d be tempted to take off the housing, waggle the valve head a bit to free it up, then stick a cheapy replacement synchronous motor on there to ensure I had heating by the end of this week, when it is going to get quite a bit colder and stay that way for a while.
But then, I am a certified bodger.