Hard to answer without test.
Ultrasonic cleaners works way higher than the agitation process that etching fluids require. The agitation in etching is "required" for the old copper that has been already removed from the enchant, to leave the surface of the board so that the process would go faster.
There is actually no need of ultra sonic as the reason of agitation is simpler than the affect of u/s. I believe that even if it works, it would be too much for this.
Hand agitation by softly moving the bowl up-down from one side is far enough.
I use air pump agitation. I have an air pump blowing air at the bottom of the bowl. The bowl is tall and thin, and the boards are hanged from the top side. The bubbles from the air comming out of a long hose with small holes, creates an agitation so efficient, that with 45 degrees of solution temperature i can complete the process in no-time... I strongly recommend this to you also.