A friend and I discussed how it would be to run tubes and solid-state side by side. The chain will go guitar - Y-cable - tubeamp - Y-cable - poweramp.
\ distrtion pedal /
I will add to that: the ABY should have a phase switch, too, because the output stage of one amp may have a different phase than the other. The Radial ABY is a great unit with a lot of useful features.
When you wrote "tube amp" did you mean "tube preamp"? If not why not just split the signal to the tube amp and let it have its own output and speakers instead of slaving it to the tube power amp. Then just run your stomp box into the power amp and its set of speakers. That way you can mix and match speaker tones too if you want.