I wonder if the siren thing varies from location to location, a good friend of mine lived right next to one and it seemed you couldn't go 15 minutes without being drown out by them heading out.
In my experience (former firefighter here), it absolutely does. It also varies by call type, time of day, etc. So if we got a call at 2:00 AM and there was no traffic on the road near the station, we might leave the station with no siren out of respect for the people trying to sleep in the homes very close to the station. This would be more true if the call was a lower priority call in the first place. OTOH though, if the call as "residential structure fire with occupants reported trapped" our focus would not be on sleeping neighbors and there's a better chance that we'd be getting on the Q pretty much right out the door.
Another factor for us was that our station was right next to an intersection that was very busy at times, and known for many traffic accidents. So any call where we had to turn left (towards the intersection) out of the parking lot, there was a better chance we'd be hitting the siren and air-horn pretty much right from the jump.
Anyway, yeah, net-net, this is going to vary based on lots of factors: department policy / culture, geography, time, traffic, etc, yadda yadda.
Q?
Other things which are bothersome about a firehouse…
• They put the communications radio on some sort of loud speaker sometimes, so you get to listen to all the calls in the city.
• They have some sort of turbine that runs a lot. Maybe a hose dryer? I haven't gone to ask, but when I used to do audio recordings there were days we couldn't record because of it.
• Their backup generator optimizes efficiency by minimizing the muffler. The tests are pretty loud.
• The building department made me block up the windows on their side because I was too close to the property line and a fire might spread to the fire station. I say if the fire department can't keep fire from coming out my window and setting fire to their building 60 feet away, that's at least partly their fault. :-)
• They are a multi-tier bureaucracy. When their tree slowly fell over on to my building it took many months to get them to admit it was their tree and maybe they should cut it down. Lots of finger pointing between the fire department and various city levels and a few "dead parrot" conversations with different functionaries.
My main concern would be all of the communications equipment they typically have. Being that close to high powered transmitters can cause annoying interference.
I know I would attempt one. Try nice and some charm and see what comes of it. May end up popular with neighbors.
You will always see the flashing lights but they have never blasted the sirens at night.