The walk isn't that hefty by Disney standards - possibly twenty minutes - but the longest part of the walk is from MGM to the resorts, from there it isn't far to Epcot at all. If you want to save both feet and time, if the boat is there as you leave MGM - catch it - its a five minute boat ride to the Swan Dolphin landing. Get off, cross the bridge to the Boardwalk, walk the Boardwalk over to the International gateway - 10 minutes. You will beat the boat to the BW landing - and probably be in Epcot before it leaves the landing. Keep in mind if you hoof it, you are tucked back behind France and Great Britain in the WS - its another ten minutes to hoof it from their to Mission Space or Mexico.
If you want to try for Fantasmic and Illuminations on the same night, you will need your running shoes - the boat won't make it. But a fit young adult probably can (as can a fit not so young adult - but this is not something couch potatos or people with young children should try). Sit towards the back of the Fantasmic theatre as close to the entrance as possible. As soon as the show is over, get moving, head out of MGM as fast as possible. Walk as briskly as you can over to Epcot and go through the International gateway. It will be dark, so you may want to scope it out earlier in the day - park and Epcot and walk over to MGM. The best seats will have been taken 40 minutes ago, but you should arrive about five minutes before the show starts.