Disney Answer: No
Unfortunately, you cannot walk from the Grand Floridian to the Magic Kingdom. Even though the two are only several hundred feet apart, Disney has made it impossible to walk between them. There is no path or sidewalk, and the two are separated by a fairly large canal that connects Seven Seas Lagoon to the Rivers of America inside the Magic Kingdom (it is also used for the parking area of the nightly Electrical Water Pageant floats).
Curiously, on the Magic Kingdom side, there is a very nice, landscaped and lighted pathway that runs from the Magic Kingdom near the monorail station out to the waterway, and then it just ends in an area with some trees and a few benches. It almost seems like the had intended to connect the Grand Floridan and the Magic Kingdom at one time, and then realized they could not efficiently get the path across the waterway. Maybe at some point in the future that path will be completed all the way to the Grand Floridan.
The good news is that the resort monorail stops at the Grand Floridian every few minutes and goes directly to the Magic Kingdom monorail station, and requires way less walking.