I would agree with you that it is unlikely that someone who is deaf would be able to pass the certification due to the necessity of being able to hear the warning claxons and horns. (I was certified through Lowes when I worked there)
At any rate, if you receive no funding or support from either the state or federal government, the applicant would be responsible for providing their own interpreter.
The ADA prohibits discrimination on the basis of disability in employment, State and local government, public accommodations, commercial facilities, transportation, and telecommunications. So as a private entity providing training, you would not be violating any part of the ADA by not providing an interpreter.
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