Pinesol will work in an ultrasonic cleaner, but there are two things you have to be cognizant of. Note that I don't know about cleaning a carb, as I never even though of cleaning a carb with Pinesol even without ultrasonic cleaning.
One is viscosity. Undiluted (how I assume you plan to use it) Pinesol has a slightly thicker viscosity. That thicker viscosity MAY reduce the effectiveness of the ultrasonic vibrations, but I don't think it would totally negate it.
That viscosity also means it will be harder/take longer to degas. If you're not familiar, usually, when using any liquid/cleaner for ultrasonic cleaning, it's best to degas the liquid first. There are various ways to do this, including letting it sit for awhile or running it for a few minutes with just the liquid. Entrained gas (in this case atmospheric oxygen) also reduces/interferes with the effectiveness of the ultrasonic waves because the microscopic bubbles collide and absorb the energy instead of the energy being directed to the material being cleaned. The higher the viscosity the liquid, the harder it is to degas.