Not in any fire department I'm aware of. Fourth alarm is generally 12 to 16 engine companies, plus aerial ladders, rescue units, one or more batallion chiefs, frequently a division chief, and a lot of ancillary gear. With New York's staffing, we're talking close to 200 guys.
In a big city you're probably right. I read they had 168 firefighters there. In suburbs with little volunteer fire companies, 4 alarm would be 4 companies -- more than that would be coming from so far away, even a major fire would likely be out before they got there.