I can see this happening after the Wild Arctic redo (which hopefully is the next thing after Mako). At this point the would have a strong number of rides (6, not including Happy Harbor or shows) and have hopefully recovered from the Blackfish disaster. Maybe they could also add a nighttime show better than Mistify or Reflections with water screens.
The path size issue shouldn't really be an issue. Most of them are large enough, besides the ones I highlighted for a parade with floats around the size of Univeral's. Those floats have some small places to crawl through as well, like where the statue is in New York. The only issue I can see is some tights turns in The Waterfront.
Oh, and the path to Bayside Stadium would need to be open to help with crowd control during the parade.