In theory yes... but it will be more of the disciplinary action against you for not showing up. After all unions are very powerful as we've seen during recent transit strike.
Thing is: living in a big city that is an island with few bridges and tunnels there is no way I could bug out. Also I don't think anyone in EMS and Fire would leave. I'm about 10 min walk from first hospital that would accept my shield for work and in case of emergency I would report there, jump on the ambulance until I can meet my home unit or supervisor. Also if not needed I can stay at JFK Airport and work there which if stranded would be a center of people dropping left and right due to their medical condition.
I think that staying behind is a better option than bugging out in my case. Hospitals/stations are set up to provide for us for extended period of time and I would do more good in the "hot zone" than out there.
It is more of the ethical thing I guess. I think you have to make a choice between: it's my job and I will do it vs I ain't getting paid enough for that.