Code of Federal Regulations (CFR), Subtitle B, Chapter III (FMCSA, DOT), Part 391, Subpart E, §391.41 Physical Qualifications For Drivers, states:
"(a) A person shall not drive a commercial motor vehicle unless he/she is physically qualified to do so and, except as provided in §391.67, has on his/her person the original, or a photographic copy, of a medical examiner's certificate that he/she is physically qualified to drive a commercial motor vehicle."
It's pretty straight forward. Doesn't matter if you are working or learning, driving on a CDL, a temporary CDL, a learner's permit, or even no license whatsoever, you
shall not drive a commercial motor vehicle unless you are physically qualified to do so and have a medical certificate that says so.
DOT guidelines to the states, the departments of motor vehicles and the various county clerks and others who administer the testing is equally as straight forward in that the guidelines simply state that in order to be
eligible for a CDL you must have had a physical within the last two years and have a DOT medical certificate confirming the examination. In addition, because of 9/11, first time CDL applicants must also present an approved form of ID, such as a passport, birth certificate or Social Security card (among others), in order to be eligible for a CDL.
Without the proper ID and medical certificate, you aren't eligible for a CDL, and without the medical certificate you certainly aren't eligible to drive a commercial motor vehicle regardless of what kind of license you have while waiting to get your CDL. I don't know how Ohio is doing things, but the guidelines to the states from the DOT say that if you don't have the proper ID and medical certificate, there's no point in testing you if you aren't even eligible for the license.