No, the turbo is working all the time, though at very low revs and small throttle openings it doesn't do a lot. Peak torque starts at 1600rpm so at that point the turbo is working flat out when the throttle is wide open.
As far as I'm aware, sport mode only alters throttle response (that is, the throttle is opened further for the same amount of pedal travel) and automatic transmission shift points - it doesn't alter the engine behaviour, just the 'feel'.
The AutoGuide.com network consists of the largest network of enthusiast-owned enthusiast-operated automotive communities.
AutoGuide.com provides the latest car reviews, auto show coverage, new car prices, and automotive news. The AutoGuide network operates more than 100 automotive forums where our users consult peers for shopping information and advice, and share opinions as a community.