No, in fact it has a 357mm lens - the 2000mm is the equivalent focal length so if you crop the 500mm lens on FF to 2000mm equivalent you're actually going to have a larger surface area captured on the FF sensor. People will always point out you get more pixels from the crop sensor but the pixels on the small sensor are in no way equivalent to the FF sensor.
Having shot with similar 1/2.3in sensors I couldn't disagree more about being 'pleasantly surprised', the noise at base iso is not good and quickly gets worse, there's almost no dynamic range to work work nor any latitude whatsoever in the raw file. Hence I'd much rather heavily crop the FF image since at least it's starting with vastly better noise control and dynamic range.