The exhaust won't work, but included with my grandpa's 1952 8n ford tractor came with an adaptor that you would replace a spark plug on one cylinder, and then pump up a tire using the unburned air fuel mixture into the tire, and running the enigne on the other 3 cylinders.
So the idea is very close to something that was actually done in the real world.
You are not the first to think of that . But I know the adaptor was somewhat common (the 8n is the most popular tractor model ever, and shared an engine with the model A) and i've never heard of issues. I'm not sure if that is because nobody talked about it though.
Yes, that's the point. You don't need it to run to fill a tire: just crank it over a few times with the starter then replace the spark plug and turn the fuel back on.
If you wanted to run the engine while once cylinder is connected to a tire then you'd very quickly overinflate it. Also you'd be running the engine without a cylinder (no spark plug) which is probably always a bad idea and in many cases straight up impossible.