Disney Answer: NO
Walt Disney World has two monorail lines, and neither of them goes to Disney’s Hollywood Studios. One monorail line goes in a loop that serves the Magic Kingdom, Contemporary Resort, Walt Disney World Transportation and Ticket Center, the Polynesian Village Resort, the Grand Floridian Resort and back to the Magic Kingdom. Technically there is a second part of that line that does the exact same loop but only stops at the Magic Kingdom and the Transportation and Ticket Center, that is the “express” monorail. The second monorail line goes from the Transportation and Ticket Center to Epcot and back, only those two stops.
Neither of those lines extends beyond Epcot to the South, and there are no plans by Disney to add additional monorail lines. However, the new Disney Skyliner connects Disney’s Hollywood Studios with 5 resorts (Disney’s Riviera Resort, Disney’s Caribbean Beach, Disney’s Pop Century and Disney’s Art of Animation resort) as well as Epcot.