It is possible. My hygienist was understanding with my tinnitus and did almost all the cleaning with the hand tools. She would have been fine with just that, but I stupidly said it was okay to use the ultrasonic for the last bit. I have a bit of a spike now. I do think earmuffs help a little bit with the ultrasonic (they don't get quite the same occlusion effect that earplugs do), but it's still very loud.
With how sensitive to sound you seem (from previous posts) I would recommend requesting a hand tools only cleaning.