Doesn't look good. Just getting from the Amtrak station to the Swan/Dolphin takes over three hours, spans over forty miles, and requires four bus changes plus several miles of walking for transfers plus a cab ride.
http://trip1.golynx.com/ntp/en/?#result_mark
Actually, travel by Lynx from either the Kissimee or Orlando requires only one change of buses (from Kissimmee, change at Osceola Square Mall) and takes about 1 hour 15 minutes to reach the Transportation & Ticket Center (about 13 miles). Total walking distance is about 600 feet. While Lynx will accept luggage, you can't have any more than you can carry yourself at any one time, and from what has been posted on these boards, Disney apparently prohibits baggage aboard its buses (perhaps Cranbiz could elaborate). You can always take a cab from the TTC (or Downtown Disney - the other WDW Lynx stop) to your hotel if necessary (much cheaper than a cab all the way from Kissimmee) to transport luggage.
For ctpooh, the TTC is relatively close to Fort Wilderness if that is your Disney resort. You can't walk it, but a cab would be short and inexpensive. I don't know what Disney policy might say about taking the ferryboat over to the Magic Kingdom entrance with luggage in tow, then taking the boat from there to Fort Wilderness (an otherwise practical way of getting there).
You will see other Lynx stops listed for WDW, but check the schedules - these are commuter bus routes which operate only twice per day and are intended to transport workers to/from their jobs (if you time it right, you can always see Disney employess lined up to catch the evening bus after work).
After arrival at your resort, when you don't have luggage, Lynx can certainly transport you off-site to Orlando destinations. No, its not always a direct trip and people shouldn't expect it to be - the public bus is not your personal automobile; It's something like going from one WDW resort to another - you have to change buses. But is is an inexpensive way to get around, and the conections are usually reasonable (conect from Lynx to the I-Ride Trolley for International Drive).
