From what I understand, It all depends on what level their Department and Dept of Health says they can operate at. CFR-D, EMT or Paramedic. In the NYC System CFR-D can not treat and release nor do an RMA. The only thing close to a treat and release or an RMA in the NYC system for the CFR-D is if the patient once identified as such decides to end the encounter by outright refusing or stopping on going assistance and either walking away or asking the members to leave the premises. This of course is dependent on the patient having decisional capacity to end said encounter. If the individual lacks decisional capacity the NYPD would be asked to respond and protect the patient from "themself" and likely assist in transport via Ambulance to the hospital
While a good number of FDNY Firefighters are trained to the EMT or Paramedic level (and some even higher) they can only operate within the scope of a CFD-D. So in NYC firefighters would have to be trained, authorized to operate by NYS Dept of Health and the FDNY and be indemnified for the EMT level care before the situation your describing being able to occur. Unless of course the NYS Dept of Health revises the rules for CFR-D and permits them to treat and release/RMA.
NOTE ***This would also likely be subject to collective bargaining between the unions and the City of New York as their scope of practice would be expanded. I also don't know how the EMS unions would react to this as it encroaches on their existing duties likely leading to more collective bargaining issues.
Hope that helps.
www.thecity.nyc