No, it doesn't save any time, if you are scooping while using the FSS after exiting the FSS you still need to line up on your destination, if you have a ship that can't handle the heat you need to move away from the star before jumping, and if your destination is behind the stars it takes far longer to get around it than it's worth, a few seconds scooping while I honk and maybe check the FSS quickly for interesting objects then moving away to run the FSS if I need to takes a matter of seconds. I can imagine the extra time wasted running the FSS while scooping and it's just not worth it!
Bascially by the time I have scooped and done a quick check of the FSS I am full so sitting there is pointless, far better to move away, which I would probably have to do anyway if a) some bodies are behind the star, very likely if FSS while in scoop range, b) my next jump destination is behind the star, very likely while in scoop range, or c) I have a not running ship and need to move out of scoop range to initiate jump.