The 1.8T is designed specifically to run on premium gas. Therefore if you put in 87 octane fuel. The engine will retard the timing to compensate. That means less overall power and slower reactions. It probably won't harm the engine but your efficiency will go down and so will your horsepower.
Let me illustrate this with a tale of my own bug. I bought my bug at auction and decided to let it piggy back on the truck to Clark VW so that they could replace the brakes under warranty and do a full inspection before I took delivery.
When I picked her up it was a balmy humid 95* so I assumed the lack of power was probably heat soak and due to the A/C running. I was dissapointed the next day when I went to work to find out that even at 65* she still felt flat and lifeless. That magic swell of boost was totally gone. She just wasnt right. I drove the tank out and filled up with 94 octane and with in about 40 miles all the power started to come back. That's when it occured to me that Clark must have filled her up with rot gut.
I haven't put in the low octane stuff since. She just hates the stuff.
I dont have a story about a turbo, but i am very anal about putting good gas into my cars. The other night, i was driving my A8 up to Mt. Hood for a night drive. I went to this Chevron in Oregon, where they have to pump your gas. I went inside because my car was being denied, so before i even paid or anything the guy started pumping gas into it. The clerk had to shut it off manually, and then we both freeked out when he put the regular 87 gas nozzle back...she knew it took premium. They gave me an octane booster and a gallon of supreme to mix it up...didnt work. The car got horrible gas mileage, like 10MPG going up the Mtn and even coming down it spuddered and had issues accelerating and harsh decleration when you released the accel pedal. I was and still am pretty upset about it. I need to go burn off the fuel and fill it with premium again.
So its not a turbo story, but its a relative to the family of VW's...and it just shows how important it is to put the right stuff in your car.