We've got the same setup as you. When the fan switch is on "auto" it will turn on and off as needed whenever the A/C or heat kicks in. When the fan switch is on Low or High, the fan runs continuously at the selected speed, but the heat or A/C will still turn on and off to maintain the desired temperature.
You're 100% right about the fan drowning out the surrounding noise, although I'm not sure it helps drown out my snoring...
I live with fear every day, and sometimes she lets me go fishing.
2015 Shamrock 23IKSS
2008 Ford Expedition EL