I can say that in New Jersey, EMS, Fire, cops, state troopers - NONE of 'em - are exempt from any traffic law. We were taught this as part of our certification process in EMS.
Though we broke the law all the time and were not held accountable, if you had even a small fender bender or (worse) caused personal injury, you were likely to get the most severe punishment allowed by law. The system looked the other way unless you were involved in an accident.
In NJ, at least, the only vehicle not subject to traffic law was one being officially operated by a US Postal Service worker. And that was due to Federal law, not State.