One issue with water-based cleaning solutions is that every trace of the water and cleaner (rinse thouroughly) must be removed from the crevices in the chain or it will cause rust and prevent chain lube from penetrating properly. I either soak the chain in a couple of changes of denatured alcohol NOT rubbing alcohol (your ultrasonic would be good for this) to dissolve the water into the alcohol which will evaporate more easily or put the chain into a 250F oven for half an hour to bake out the water. Then promptly lubricate the chain to keep it from rusting; the lube will flow well if you hit the chain while it is still warm.

Rather than put the solution directly into the ultrasonic I put an inch or two of water into it and put the solutions into Pyrex beakers or coffee cans and place them into the water. The ultrasonic vibrations will couple into the solutions via the water.