Disney Answer: No
While the entrance to Disney’s Caribbean Beach Resort is only a hundred yards or so away from the back side of Epcot, there is no way to walk from Caribbean Beach to Epcot directly.
If it were a dire emergency and you needed to walk, you could make it. Across Buena Vista Drive from the Caribbean Beach, there is a sidewalk that starts just west of the RCID Emergency Services building. That sidewalk will take you past the Speedway gas station and goes to Epcot Resorts Blvd. Once across Epcot Resorts Blvd, the sidewalk forks, and one path will take you into the parking lot for the Boardwalk Inn. From there, you can walk to the Boardwalk Inn, down to the Boardwalk and into Epcot. Taking this walk is dangerous, as there is going to be a lengthy area where this is no sidewalk and you will have to cross Buena Vista Drive in an area where there are no crosswalks and the lights are not made for pedestrians.
So, while you technically can walk from Caribbean Beach to Epcot, there is no safe way that you can do it.