I've done Euro Delivery with BMW and it was a lot of fun. I'm waiting on an allocation for an A5, and am also considering Euro delivery, but it's not a very good deal right now, because Audi is not offering a discount at this point on the A5 (it's 5% on most models) . Since you need to pay for the car about a month ahead of delivery (I don't know exactly how far out Audi requires, but it's something like that), and since you won't get the car for a month or so after Euro delivery, you are essentially paying for your car for two months, while only having the use of it for a week or so in Europe. The discount would help make up for that loss of use of the car.
It's still a great thing to do, and a good excuse to do a driving vacation in Europe, if you're OK with the deal. Personally, I would plan a less urbanized tour if you do Euro delivery. Most city hotels have limited parking in VERY tight parking garages, which makes me nervous with a new car. Navigating a large European city can also be challenging if you haven't driven there before and are trying to get into the tourist areas, which are usually in the center of the city, only reached via narrow, twisting, streets.
Certainly check out the Audi FAQ on Euro delivery if you haven't already: