Your car can't tell if the tires are all "new" or not. But it can tell "turns per mile" which is related to the circumference of the tire. That is what matters to your magical quattro (torsen) differential.
Long story short: Audi's official recommendation is that the tires are "the same" circumference. On some models in the past they have further specified it be "within 4/32" of tread depth", which you can mathematically convert to keeping all the tires within 1% circumference of each other or thereabouts. So if the rest of the tires are at least 6/32" tread depth, you can run a new one (10/32) in the mix. No problems. If 2 of them are 6/32" and two of them are new, you're still good.
But if the fronts are at 4/32", you probably should not have 2 new ones one the other axle. Just replace them all, 4/32" is about done anyway. Save them for spares if you wish. The torsen differential does not have clutches, but it does have very high friction worm gears which will create a lot of heat and wear if they are asked to work constantly. Not to mention the all-important magical friction washers. So it will deal with "whatever" for a short time. Even towing 2 wheels down (THE HORROR). But long term, stuff needs to match up.
So the only reason to get Tire Rack to shave a tire for quattro match-up would be if you have 2 tires that are 4 or 5/32". And if that is the case, and you *really* must only buy 2 tires, have them shave the new ones to be 8/32". Not 4/32", that's insane. 8/32" will stay within the 4/32" recommendation and will avoid flushing gratuitous amounts of cash on pre-worn-out tires.
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