Nope. The bus that leaves RIGHT outside Amtrak is bus 40. That will take you straight to Universal Studios and does NOT stop near Sea World. Bus 50 does, but it doesn't stop anywhere near the Amtrak station. You have two options if you choose to take the bus ...
Take the NORTH bound 40 to Lynx Central Station and transfer to the 50. Bus 40 operates once an hour in each direction. The north bound typically is at the top of the hour and the southbound is typically at the bottom of the hour.
If you miss this bus by mere minutes, you can walk about a half mile East to Orange avenue where you can catch the 7 or 11 north to the LCS and get on the 50.
If you have any inclination to ride Lynx, become intimately familiar with the appropriate routes and the website. If you have a smart phone with GPS. you can follow your progress and map your routes with google maps.
Orlando is the best station. There is more activity there. From either station a cab will cost around $50-$60 but will make that 2 hour bus trip in about 30 minutes tops.