Well, I'm no EE, but it seems to me that electricity always takes the easiest path. If another amp is connected to the output of the first amp(at the speaker terminals) the speaker has an impedance load of about 8 ohms, and the other amp has an output impedance of near zero ohms. Now, I don't know how an output impedance works in reverse, but it seems to me that the majority of the power will be diverted into the non-used amp, and try to drive it in reverse. I don't know if this would do anything to the output transistors or tubes. I do know that if the non-used amp is a transformer coupled tube amp, that the driving amp will "see" the load characteristics of the other tube amp's output transformer, and it will act like an inductor in the crossover network. This will screw up sound for sure. And if any damage may occur, that would be even worse than bad sound.
If you want to use the same speakers for 2 different systems, it is much better to get a switch box with 2-in and 1-out, and switch to the one you want to use. It may have some small sonic affect, but not near as much as loading the output of your amp, with another amp's output stage. Any parts in the other amp that can react to the signal, will react to the signal, and will cause changes in your music at the very least, and possibly damage something. Not sure about that part of it. There are just some things that you don't do.
If you want to use the same speakers for 2 different systems, it is much better to get a switch box with 2-in and 1-out, and switch to the one you want to use. It may have some small sonic affect, but not near as much as loading the output of your amp, with another amp's output stage. Any parts in the other amp that can react to the signal, will react to the signal, and will cause changes in your music at the very least, and possibly damage something. Not sure about that part of it. There are just some things that you don't do.