Yes, you can. You just need to add an international plan (if you haven't already). If you don't have a plan, AT&T will kill you with data usage costs.
The AT&T agent probably wasn't lying to you in the strictest sense of the word. Most of your phone's functions will roam seamlessly while you're in Europe without needing to take any action at all. It's just that you'll be charged a higher rate to access them.
You can sign up for some optional services, like
AT&T World Traveler for $5.99 per month, to get cheaper voice airtime while traveling internationally. You can use AT&T's website to compare the roaming airtime rates with and without the World Traveler plan in each of the countries you plan to visit, to determine whether you expect make enough calls for the up-front $5.99 per month cost to be offset by the reduced calling rates.
Either way, if you place voice calls on your iPhone using an AT&T SIM while you're outside the USA, your airtime bill
will be significantly higher than it is while you're inside the USA - if it isn't already obvious to you, remember that none of your plan's regular included minutes apply to international roaming.
On the data side, if you don't take any action, you will automatically pay $0.0195 per kilobyte for data usage while outside the USA. AT&T offers 4 eligible international data plans in 65 countries - $25 for 0 up to 20 MB, $60 for 0 up to 50 MB, $120 for 0 up to 100 MB, and $200 for 0 up to 200 MB. Overage fees on any of these plans is $0.005 per kilobyte within those 65 countries. Alternatively, you can also set the headset to block data entirely while roaming.
All of AT&T's optional international roaming plans (both data and voice) can be switched on and off any time, without adding anything to your long term commitments.
