Yes it will. Steaming of any kind will require data. Resolution will play a big factor the higher the resolution the more data it uses. Generally HD 2 hour shows will use 2-3GB alone, but SD will use about 500-700mb.
Anything you use your internet connection for will count as data. There are no "free sites", Amazon, Netflix, Hulu all will count against your data. The only exception is if you are on a plan that includes a "Free Zone", data used during those times are not counted.
I stream movies from Amazon, Netflix and some other location and most of the movies they offer are not HD movies. Depending on your alloted data from Exede you should not have trouble going over your base amount unless you watch movies all the time.