If you put a TV in a Faraday cage that blocked the relevant radio spectrum, would there be no static on it? I expected the answer to be a quick Google, but it wasn't.
That is a good question, but I suspect if you tried this in real life it would still show static.
The waves are amplified with a circuit that attempts to find a signal even if it's very weak (so you can get a picture even if you're close or very far from the tv station)
At a certain point, the electromagnetic field from the running TV itself would start to get picked up
I suspect a better thought experiment would be if you just disconnected the input and amplification circuit entirely from the CRT tube, in which case you would probably just get white as the electron beam scans back and forth without any modulation.
Likely a uniform white picture since the impedance of the input wire is too high for ambient noise on the line to result in any differentiated interlacing.
You'd still see static from the TV itself and any radiation that passed in to the cage. It's not a perfect EM blocking device like TV shows and movies would have you believe.