Yes.

A paint booth…  any paint booth…  anywhere… needs a fire suppression system. If you don’t have a fire suppression system in your booth, one way or another, it’s violating code. Remember, you are spraying PAINT and collecting potentially flammable and/or explosive materials in that space. If your paint booth doesn’t have a fire suppressions system, then perhaps the inspector did not notice or something slipped through the cracks. You should install it immediately and avoid the potential risks for your own sake and the sake of your employees.