Yes, all the 4th floor rooms out on the on the east-facing side of the far east wing have balconies! Have you booked a balcony room? Here's a picture of the furthest east wing, copied from a post by DISer BLONDIE on another thread. Note the darker colored balconies on each room of the "finger" of the wing on the 4th floor .
If you are on the other side of the hall of the wing though, you won't see Epcot from your room, it will look west towards the inner wing, even though you are int eh east wing you'd be ont he west-facing side of the hall. You'd the wing across from you and Swan towards your left , across from the Dolphin and also possibly the Grotto pool and MGM in the distance ~ the further out towards the end of the finger of the wing you are.
The Epcot views from rooms on the east facing side of the hall on the far east wing are pretty much unobstructed.

Also note though that there are 4th floor rooms without balconies in east end of the hotel on the "main" part of the building...in the picture to the right of the finger/wing with the balcony rooms.
The Dolphin is such a great hotel and a fatastic location, I think you'll enjoy it tremendously no matter what your room/view ends up being!! Have fun!!
