Now, as to the OP.. that's not a simple question. A restrictive intake reduces the absolute pressure of the air entering the turbo. That's simple physics and how throttles work.
Turbochargers operate differently at different pressure ratios (in/out) and at different speeds. There's a litany of factors involved here and a thorough answer would require lots of measurement and plotting on the compressor chart for the particular turbocharger in question. I'm not going to do all of that work. In the hypothetical, higher incoming absolute pressure will require less speed from the compressor to reach the same target output pressure. Since these cars have intelligent boost control and a boost target, the car will "ease off" the turbo once that pressure is reached. A higher inlet pressure will result in the same output pressure with less turbine speed. In theory, this could slightly extend the life of the turbo bearings. In practice, it's like a shortcut that saves 20 feet of driving on a 2000 mile trip, barely worth it.
That's what happens on a stock tune.
On a performance tune things are different. Winter air is more dense than summer air. The car, in stock form, doesn't really capitalize on that. It hits the target and opens the gates . That's why your car performs similarly in summer and winter while stock (up to the limits of physics). They set the targets low enough to be usually achievable at sea level and 70F. We tune our cars to achieve target at about 1000ft elevation and 100F (typical conditions in Alabama). We also give a more room beyond that so you can benefit from cold winter air if it's available.
Remember when it first got cold and a couple people had overboost issues with our tune that we released in the summer? Bingo.. this is precisely why. We expanded those boundaries a bit more to further compensate for winter conditions. It's all modeled in the ECU, but sometimes even the best engineers (a combination of Bosch, Audi, APR and the turbo manufacturer in this case) can't always nail the prediction math 100%. (Obviously, Audi didn't come to us to work on this. But, Audi, Bosch and the turbo manufacturer did the measurements and constructed the model from them.)
Back to your question: A tuned car will use up some of that "room" to take in more air from a less restrictive intake (if you actually have one that is less restrictive.. we haven't seen one yet for these cars) and give you more performance. The turbo will spin about the same speed it did with your stock airbox, but you'll get a few more HP out of it.
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