The shuttle service will provide you with transportation to any of the parks or hotels on-property.
While the shuttle will drop you off near the gate (in the bus parking aras) of the other three parks, if you ask to be brought to the Magic Kingdom they'll drop you off at the TTC.
Alternatively, you can ask to be brought to the Contemporary and walk over, or even the Grand Floridian and take the monorail one quick stop. (I presume that the Alamo shuttles use the rear access road over to Bear Island Road and turn north onto Floridian Way where it's still a 2-way street)
Another alternative if you don't want to be at the will of the Alamo shuttle would be to change your drop-off to be at the Dolphin. You drop it off with the valet out front, and then walk over to the Dolphin bus stop and get on a MK-bound bus. (Or if you decide to go to Epcot or the Studios that day, you can walk or take the boat from there)
-Rob