Yes it is possible. Fantasmic is about 20 minutes long, and Illuminations always goes off at 9pm. So there is plenty of time. There are many ways to get there. The easier, but not the shortest time-wise, is to walk. There is a walkway once you exit MGM(just follow the walkway and you'll see signs) that takes you to the Boardwalk Resort. It's about 15-20 minute walk there. Then follow that path to the Boardwalk. Then from the boardwalk, you follow that around to the International Gateway entrance to Epcot, which is about a 5-10 minute walk. This entrance drops you off right at the World Showcase. You can grab a spot, it won't be the best spot and there might be a few rows of people infront of you, and relax until Illuminations.
There are boats the also run to the resorts and Epcot, but that gets a huge line at MGM, and there are 3 stops it makes along the way.
I'm not sure how the buses work or if there's a bus that goes to Epcot, but those lines will be long too, unless you can run right out of Fantasmic to the bus stop.
The walk is probably your best bet. It's a nice walk too. My family and I have stayed at the Boardwalk many many times, and the walk is relaxing and quiet.