I picked up some arrows for dirt cheap today and they have 2" vanes already on them. Without considering the weight or spine of the arrow, will the 2" vanes fly the same as the 4"?
Yes, but 2" vanes usually have a higher profile so you want to make sure there is no contact with any part of the bow.
At 20 yds or less they will group pretty close together but the farther back you move the 4" vanes will start dropping. At more than 40 yds it will become a pretty significant drop. You shouldnt mix arrows with different vane lengths because your sight pins will only be accurate for one or the other.