No.
it doesnt give any extra grip at all.
But your very right it doesnt make a huge difference in the real world.
In a nutshell all cars need to have a differential - because when you go around a corner, the outside wheel travels further than the inside wheel, so the wheels need to spin at a different rate.
So, when your delivering power to these wheels, the power can, in certain circumstances, be unevenly biased.
Imagine going around a wet roundabout, flooring the throttle, 9 times out of 10 the inside wheel will start spinning, which will result in the back end kicking out.
A Limited Slip Differential does exactly what it says on the tin, it limits the amount of slip to any wheel, so in our example, the inside wheel could still spin, however the outside wheel will still have *say* 25% of the power.
So, if you want nice big controllable powerslides, like in drifting, you need a LSD. If your very heavy footed in very bad weather, a LSD may counteract your bad driving to a degree.
However, when I tried a sport, i found it 'numbed' the connection with the road somewhat, the SE I found had more feel to the clutch and gearbox, and I seemed to find it easier to gauge when i could put the power down much better compared to the Sport.
But its horses for courses, it all comes down to what you want out of a car - for me a few splashes of Aluminium and a LSD didn't warrant waiting for a sport when the right spec car turned up as an SE.
I would advise the same to Jammie, buy the car based on Spec/History/Condition rather than being too specific.. otherwise he could be shopping for a long time