No, and even better, Apple says these calls won't be eating up your voice minutes either. FaceTime calls are made over WiFi only, so you'll be free to make them anywhere you can find a WiFi signal (like Starbucks, perhaps?), without using carrier minutes, or any MB from your smartphone data plans. However, you'll need to start taking into account your data budget when (and if) AT&T starts allowing FaceTime calls over 3G. I'd stick to WiFi either way if I were you.
One of the major selling points of the iPhone 4 is the arrival of FaceTime video calling. The feature uses the iPhone's front and rear cameras to make face-to-face video calls, which can be great for families chatting from long distance, or saying hi to a faraway friend. But with the newly lowered limits on AT&T's data plans, you may be wondering: will these FaceTime calls be using up my data allowance?