No.
In the United States, there is only an air brake RESTRICTION. If the CDL applicant does not take the written air brake exam when applying for a CDL or does not take the road test with an air brake equipped vehicle, the CDL will have a restriction L on the CDL, meaning vehicles without air brakes. This restriction only applies to vehicles that require a CDL. For example, a driver with a CDL and air brake restriction can still legally operate a box truck with a GVWR less than 26,001 lbs. with air brakes, because the box truck does not require a CDL.