It certainly can be done. DH & I did it April 2004. We watched Illuminations from the bridge near International Gateway. As soon as the show ended (about 9:15) we walked quickly toward Boardwalk, cut over to the DMGMS walkway, and got to Fantasmic 5 minutes before showtime. A couple people on the way tried to tell us it was faster to take the boat, well, we made it before the boat. We walked quickly, but didn't need to run.
It was one of the neatest things we've done. We weren't sure it we would make it, but we wanted to try. It is only possible on nights that Fantasmic is shown twice. We walked from the Studios to EPCOT earlier in the day to time ourselves and make sure we had the route right. (took a bus from our resort to the Studio's early one afternoon, hung our there a little while, then walked to EPCOT earlier enough that we could go have dinner somewhere and rest up if we needed to.) Also, I don't recommend it with children. It was just DH & myself when we did it.
I recommend trying it!
Lori