You already know it's not recommended. My wife takes a bubble bath at least 2x a week. When my son was about 8 it would generate so many he could hide under them. Anyway, once or twice a year we ( I ) run electric dishwashing liquid and a gallon of vinegar thru the system; rinse twice and it works a. ok. Our whirlpool tub is 9 years old and works perfectly.Can you hurt a whirlpool tub if you put bubble bath in the water?
depends how long you want to be mopping up bubbles from the house-yard-garage-basement-neighbors house-and so on,when the bubbles go through the pump it would be one of the best bubble shows seen in years,it would make Lawrence Welk jealous (old tv show from the fifties%26amp;sixties)
After a while the filter gets messed up. But you can do it a couple times and you'll be okay.