System to system

No, the unpowered/not used amp would load down the powered amp and depending on the circuit could actually damage it.

No, you can't. The reason is that you will have the amp's output impedance in parallel with your speaker AND the other amp's output impedance. This will cause too many issues to be useful.

I assume your Sansui has crappy wire jacks for the speaker leads. If you can adapt them to bananas and use banana terminations on your speaker cables, it will be easy to just swap amps when necessary.

Look to see if your Sansui has pre-out jacks so you can just run it to your Cary preamp and have the tuner that way. Some receivers had pre-outs and others didn't so you have to check. This would be the cleanest (assuming your Cary has two extra inputs for both the tuner and Sony/Lite).

Arthur

Yes, you can!
I'm not sure about tube amp but you can do this with two SS amps connecting speaker between +outputs of both amps and shorting -outs (grounds) together. Since this is a little similar to bridging amps (but no phase reversal) amps have to be bridgeable (single ended outputs)and have similar power ratings. Both amps have to be on and the speaker will receive difference of both outputs. You can even play both at the same time. I've never tried this (strange application) but don't see any reason why it wouldn't work. Unpowered amp can get damaged but it's the same with two monoblocks bridged for more power. On the other hand it's always better to keep things standard and avoid experimentation.

Not a good idea to hook your speakers up in parallel to two amplifier outputs. That one amp is off will not negate the difference in impedance caused by this setup. What you are trying to do, I assume, is have the capability of driving your speakers with either one amp or the other. A solution may be to make or buy an "A B" switch box. Make sure the switching is 'break before make' and the contact resistance is spec'd very low - a few milliohms. This will allow you to do what you want to do without affecting your system in a negative manner. And don't flip the switch with power on to either amplifier.