With the gas pedal to the floor the sport and economy shift
points are the same. So, sport mode can not make your maximum
acceleration any faster.

At part throttle, the sport mode holds the shifts a bit longer so
the engine revs a bit higher before the transmission shifts gears.
I suppose this could result in slightly faster acceleration in sport
mode at part throttle (given the exact same throttle position). The
higher engine revs may also keep the turbo spinning (if you have one)
so the car might respond quicker with sport mode if you were to
suddenly floor it.