Not that I wouldn't mind trying this if I was handy and knowledgeable with electronics and could take pride in the build, but...Yes, yes and also an ABY* is not a mixer in any circumstance, it's a (passive) switchable splitter. If you put a strong buffer before the split, the feedback would stop (in most circumstances) but you'd get approx. nothing from the Rat. (*a normal one without resistors, some might have them even though they reduce performance in the main intended use.)
The cheapest correct way to do this is use something with separate buffered dual outputs, say a stereo chorus (off), or at least a good buffer and a Y cable to split the signal (this will still scream a moment when you cut off the power). Then remix it with a 100K potentiometer in a box. Place another buffer after this for long cable runs.
You only lose dynamic interplay that is caused by loading down the guitar signal, the dynamics of normal level control remains. You can't load down the signal and still do a true clean mix, the clean is muddied. Also, the clean part of the mix is affected more by the guitar volume. It's kind of reverse-dynamic because playing louder brings out the clean and letting off brings out the dirt, if the gain is that high.Not that I wouldn't mind trying this if I was handy and knowledgeable with electronics and could take pride in the build, but...
He could go the easy route and get a Boss LS-2 Line Selector, which allows 5 different combinations of its two loops, including running them in parallel, which would solve the OP's dilemma. One of the loops would have the Rat and the other would have nothing (defaults to the straight signal). Since each loop has its own level control, you can blend in the desired amount of original signal with the desired amount of Rat.
Though, if anyone tries this concept with a fuzz or treble booster, since the LS-2 is buffered, you lose the dynamic interplay between your guitar's volume knob and the fuzz or treble booster (yes, I learned that the hard way.)
The LS-2 can turn an amp's series effects loop into a parallel loop, so this is that same principle, just in front of the amp and not in its loop.