Experience with using AT&T (GSM) iPads in Europe?
Yes, the GSM iPad will work in Europe.

Generally, there are no residency requirements to purchase a Pay As You Go (pre-pay) plan. Some countries may require identification and a local address while others allow you to pay cash and walk out of the shop with the SIM. If you try to buy a contract, you will need bank details and a credit check which would require residency.

The specifics can vary from country to country and carrier to carrier as each have their own policies. The best advice is to check the carriers in the country where you are going and see what their policies are. Then you'll be most prepared when you walk into the shop.