Yes, the fuel gauge is active ALL the time - whether the car is on or not.
Let me give some more background: I just had the fuel pump replaced, which includes the sending unit for the fuel gauge. When I picked up the car from my mechanic, I noticed the fuel gauge was giving a reading even before I started the car.
I've had the car for 8 years, but I honestly can't tell you if this is the way the fuel gauge has always behaved, or if this is something new since the fuel pump was replaced.
As far as I know, the analog-style fuel gauges on most cars are only active when the car is on (or the key is in the Accessory position).
So I basically just need someone to give me a definitive answer: on a 1998 Legacy GT wagon, is the fuel gauge supposed to be active all the time?