Michael,
Just like a flashlight, there is always some scatter in the radar beam. The cone widens the further you get away. Just like every other radar in the world, it CAN be detected much further out than what the return would be to the sender. So, yes, you could get a warning before you see the police car.
Like Robert said, there is a procedure most departments use though. The first is the visual estimate. It's surprisingly accurate within 5 mph or so of the radar readout after you've done it a while. In most cases, though, all the radar needs is 30 seconds or so (usually less though) and a good clear tone on the audio and your busted. Obviously I haven't used the newest radar on the market so I'm going to take a leap here and assume that advances in technology have helped in the traffic radar arena too.
Now imagine your running down the highway. You get a flicker on your detector and it goes out. Not a real strong signal. Ok, a little further and you get another flicker. Now your in a valley behind a hill. Over the top of the hill you go and your detector blasts in your ear. Dude, Too late, you're busted! It's that fast. Remember, there are plaenty of things out there that will produce false positives on detectors and they don't have the advantage of having a doppler tone to discriminate. A detector is simply a receiver.
Caleb: You better believe these guys are sneaky! You don't know the half of it! BTW: I got busted myself outside Enid by OHP. I had just come off of OK 74 and got up to speed, set my Cruise Cotrol and saw the lights in my rear view mirror. I never saw him. He was a nice guy though and we both got a chuckle out of it, he took a look at my GRLevel3, gave me a warning and I was off again.