No, it's way to risky. I don't know how the Niles is made, so I wouldn't risk it. A lot of switches are made with solid state only in mind. And you did mention tubes. First off, with any switch, the plus and minus both should be isolated, through the whole switching device.
With tube amps involved, there should be a load resistor on a tube amp when the switch is in the other amps position. That way there would be a lot less risk. Even if your careful enough to not make a mistake. If you switch off the tube amp to turn on the SS amp for the TV, the switch needs to have a load(load resistor) on the tube amp. The reason would be the tube amp power supply would hold a lot of voltage stored in it when turned off, and any little noise could cause the output transformers to short out. This noise could happen during the switching, or a tube or other part while cooling down. It needs a dummy load, or speaker load on it all the time, just in case there is that voltage stored in it. It is quite common for tube amps to hold that reserve voltage, for unknown lengths of time. To many unknowns make this a risk. That relay system might have zero protection for this.
