No that’s no the “pink milk shake”.
You’ll know because the oil will make everything gooey and make one hell of a mess. If it’s ran that way very long, your transmission dies an untimely death.
20 years ago when Freightliner was building all the RV chassis they had a bad run of radiators that caused a lot of Allison transmission‘s to get pulled out of motorhomes. I think I helped swap out at least five or 10 of the damn things. Hell of mess when those two fluids mix.
Just change the radiator. It’s super easy. Easily the most simple radiator swap I’ve ever seen from cars,trucks, and semi’s. It’s only like 4 or 6 bolts and has its own built in hangers. Frickin awesome setup that Toyota put together. Hell of cheap too. Like $130 from the dealer. That’s only like 2-3 tanks of gas depending where you live. Even the AC condenser is cheap. Just change it all. You won’t regret it.
Even if you can’t/don’t want to wrench yourself, I highly doubt the entire job would cost more than 350-400$ for the radiator. Still super worth it.
Odds are your radiator is slightly plugged anyway from the poor placement of the Heater valve creating corrosion in the system by allowing a constant air bubble in the less than perfect systems. The only real thing I feel like Toyota messed up on on these rigs really.